subject:(Automorphic Forms Representation Theory)

University of Oklahoma

1. Wagh, Siddhesh. MAASS SPACE FOR LIFTING TO GL(2,B) OVER A DIVISION QUATERNION ALGEBRA.

Degree: PhD, 2019, University of Oklahoma

► Muto, Narita and Pitale construct counterexamples to the Generalized Ramanujan Conjecture for GL(2,B) over the division quaternion algebra B with discriminant two via a lift… (more)

Subjects/Keywords: Number Theory; Automorphic forms; Representation Theory; Maass forms

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APA (6^th Edition):

Wagh, S. (2019). MAASS SPACE FOR LIFTING TO GL(2,B) OVER A DIVISION QUATERNION ALGEBRA. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/321131

Chicago Manual of Style (16^th Edition):

Wagh, Siddhesh. “MAASS SPACE FOR LIFTING TO GL(2,B) OVER A DIVISION QUATERNION ALGEBRA.” 2019. Doctoral Dissertation, University of Oklahoma. Accessed March 07, 2021. http://hdl.handle.net/11244/321131.

MLA Handbook (7^th Edition):

Wagh, Siddhesh. “MAASS SPACE FOR LIFTING TO GL(2,B) OVER A DIVISION QUATERNION ALGEBRA.” 2019. Web. 07 Mar 2021.

Vancouver:

Wagh S. MAASS SPACE FOR LIFTING TO GL(2,B) OVER A DIVISION QUATERNION ALGEBRA. [Internet] [Doctoral dissertation]. University of Oklahoma; 2019. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/11244/321131.

Council of Science Editors:

Wagh S. MAASS SPACE FOR LIFTING TO GL(2,B) OVER A DIVISION QUATERNION ALGEBRA. [Doctoral Dissertation]. University of Oklahoma; 2019. Available from: http://hdl.handle.net/11244/321131

Harvard University

2. Raskin, Samuel David. Chiral Principal Series Categories.

Degree: PhD, Mathematics, 2014, Harvard University

URL: http://nrs.harvard.edu/urn-3:HUL.InstRepos:12274305

►

This thesis begins a study of principal series categories in geometric representation theory using the Beilinson-Drinfeld theory of chiral algebras. We study Whittaker objects in… (more)

Subjects/Keywords: Mathematics; Algebra; Algebraic geometry; Automorphic forms; Geometric Langlands; Representation theory

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APA (6^th Edition):

Raskin, S. D. (2014). Chiral Principal Series Categories. (Doctoral Dissertation). Harvard University. Retrieved from http://nrs.harvard.edu/urn-3:HUL.InstRepos:12274305

Chicago Manual of Style (16^th Edition):

Raskin, Samuel David. “Chiral Principal Series Categories.” 2014. Doctoral Dissertation, Harvard University. Accessed March 07, 2021. http://nrs.harvard.edu/urn-3:HUL.InstRepos:12274305.

MLA Handbook (7^th Edition):

Raskin, Samuel David. “Chiral Principal Series Categories.” 2014. Web. 07 Mar 2021.

Vancouver:

Raskin SD. Chiral Principal Series Categories. [Internet] [Doctoral dissertation]. Harvard University; 2014. [cited 2021 Mar 07]. Available from: http://nrs.harvard.edu/urn-3:HUL.InstRepos:12274305.

Council of Science Editors:

Raskin SD. Chiral Principal Series Categories. [Doctoral Dissertation]. Harvard University; 2014. Available from: http://nrs.harvard.edu/urn-3:HUL.InstRepos:12274305

3. File, Daniel Whitman. On the degree 5 L-function for GSp(4).

Degree: PhD, Mathematics, 2010, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1279567891

► In this dissertation I establish a new integral representation for the degree five L-function for the group GSp₄. Let F be a number field and… (more)

Subjects/Keywords: Mathematics; automorphic forms; representation theory; number theory

…proposed several conjectures relating automorphic representation theory to number theory [25… …determine whether it is the L-function of an automorphic representation. Such a result is known as… …representation π = ⊗v πv of an adelic algebraic group G(A) is automorphic. The converse… …Dirichlet series that are twisted by GL2 automorphic forms. Suppose that f is a cuspidal elliptic… …space of automorphic forms. 1.3 The Degree Five L-function In [1] Andrianov and…

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APA (6^th Edition):

File, D. W. (2010). On the degree 5 L-function for GSp(4). (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1279567891

Chicago Manual of Style (16^th Edition):

File, Daniel Whitman. “On the degree 5 L-function for GSp(4).” 2010. Doctoral Dissertation, The Ohio State University. Accessed March 07, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1279567891.

MLA Handbook (7^th Edition):

File, Daniel Whitman. “On the degree 5 L-function for GSp(4).” 2010. Web. 07 Mar 2021.

Vancouver:

File DW. On the degree 5 L-function for GSp(4). [Internet] [Doctoral dissertation]. The Ohio State University; 2010. [cited 2021 Mar 07]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1279567891.

Council of Science Editors:

File DW. On the degree 5 L-function for GSp(4). [Doctoral Dissertation]. The Ohio State University; 2010. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1279567891

Temple University

4. Daughton, Austin James Chinault. Hecke Correspondence for Automorphic Integrals with Infinite Log-Polynomial Periods.

Degree: PhD, 2012, Temple University

URL: http://digital.library.temple.edu/u?/p245801coll10,162078

►

Mathematics

Since Hecke first proved his correspondence between Dirichlet series with functional equations and automorphic forms, there have been a great number of generalizations. Of… (more)

Subjects/Keywords: Mathematics; automorphic forms; automorphic integrals; hecke correspondence; number theory

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APA (6^th Edition):

Daughton, A. J. C. (2012). Hecke Correspondence for Automorphic Integrals with Infinite Log-Polynomial Periods. (Doctoral Dissertation). Temple University. Retrieved from http://digital.library.temple.edu/u?/p245801coll10,162078

Chicago Manual of Style (16^th Edition):

Daughton, Austin James Chinault. “Hecke Correspondence for Automorphic Integrals with Infinite Log-Polynomial Periods.” 2012. Doctoral Dissertation, Temple University. Accessed March 07, 2021. http://digital.library.temple.edu/u?/p245801coll10,162078.

MLA Handbook (7^th Edition):

Daughton, Austin James Chinault. “Hecke Correspondence for Automorphic Integrals with Infinite Log-Polynomial Periods.” 2012. Web. 07 Mar 2021.

Vancouver:

Daughton AJC. Hecke Correspondence for Automorphic Integrals with Infinite Log-Polynomial Periods. [Internet] [Doctoral dissertation]. Temple University; 2012. [cited 2021 Mar 07]. Available from: http://digital.library.temple.edu/u?/p245801coll10,162078.

Council of Science Editors:

Daughton AJC. Hecke Correspondence for Automorphic Integrals with Infinite Log-Polynomial Periods. [Doctoral Dissertation]. Temple University; 2012. Available from: http://digital.library.temple.edu/u?/p245801coll10,162078

University of Minnesota

5. Zhang, Lei. Automorphic forms on certain affine symmetric spaces.

Degree: PhD, Mathematics, 2011, University of Minnesota

URL: http://purl.umn.edu/109867

► In this thesis, we consider automorphic periods associated to certain affine symmetric spaces such as the symmetric pairs. In this thesis, we consider automorphic periods… (more)

▼ In this thesis, we consider automorphic periods associated to certain affine symmetric spaces such as the symmetric pairs. In this thesis, we consider automorphic periods associated to certain affine symmetric spaces such as the symmetric pairs (Sp4n; ResK=kSp2n) and (GSp4n; ResK=kGSp2n); where k is a number field and K is an Etale algebra over k of dimension 2. We consider the period integral of a cusp forms of Sp4n(Ak) against with an Eisenstein series of the symmetric subgroup ResK=kSp2n. We expect to establish an identity between this period integrals and the special value of the spin L-function of the symplectic group. In the local theory, using Aizenbud and Gourevitch's generalized Harish-Chandra method and traditional methods, i.e. the Gelfand-Kahzdan theorem, we can prove that these symmetric pairs are Gelfand pairs when Kv is a quadratic extension field over kv for any n, or Kv is isomorphic to kv x kv for n <_ 2. Since (U(J2n; kv(p28; )); Sp2n(kv)) is a descendant of (Sp4n(kv); Sp2n(kv) #2; Sp2n(kv)), we prove that it is a Gelfand pair for both archimedean and non-archimedean fields. According to the Yu' construction in [76] of irreducible tame supercuspidal representations, we give a parametrization of the distinguished tame supercuspidal representation of symplectic groups in this thesis. Applying the dimension formula of the space HomH(#25;; 1) given by Hakim and Murnaghan [28], we prove that if (G;H) is the symmetric pair (U(J2n;Kv); Sp2n(kv)) there is no H-distinguished tame supercuspidal representation, where Kv is a quadratic extension over kv. In addition, for the symmetric pair (Sp4n(kv); Sp2n(Kv)), we give the sufficient and necessary conditions of generic cuspidal data such that the corresponding tame supercuspidal representations are H-distinguished. Note that our case is the first case worked out with none of G and H being the general linear groups. Furthermore, motivated by a sub-question, we also give an example for the distinguished representations of finite groups of Lie Type in a low rank case. In particular, we show that #18;10 is the unique SL2(Fq2) distinguished cuspidal representation of Sp4(Fq). Note: See PDF abstract for the correct interpretation of the mathematical symbols.

Subjects/Keywords: Automorphic forms; Distinguished tame supercuspidal representation; Gelfand pairs; Number theory; special value of L-function; Mathematics

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APA (6^th Edition):

Zhang, L. (2011). Automorphic forms on certain affine symmetric spaces. (Doctoral Dissertation). University of Minnesota. Retrieved from http://purl.umn.edu/109867

Chicago Manual of Style (16^th Edition):

Zhang, Lei. “Automorphic forms on certain affine symmetric spaces.” 2011. Doctoral Dissertation, University of Minnesota. Accessed March 07, 2021. http://purl.umn.edu/109867.

MLA Handbook (7^th Edition):

Zhang, Lei. “Automorphic forms on certain affine symmetric spaces.” 2011. Web. 07 Mar 2021.

Vancouver:

Zhang L. Automorphic forms on certain affine symmetric spaces. [Internet] [Doctoral dissertation]. University of Minnesota; 2011. [cited 2021 Mar 07]. Available from: http://purl.umn.edu/109867.

Council of Science Editors:

Zhang L. Automorphic forms on certain affine symmetric spaces. [Doctoral Dissertation]. University of Minnesota; 2011. Available from: http://purl.umn.edu/109867

6. Lim, Li-Mei. Multiple Dirichlet Series Associated to Prehomogeneous Vector Spaces and the Relation with GL3(Z) Eisenstein Series.

Degree: PhD, Mathematics, 2013, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:320644/

► In this disseration, we generalize the classical result relating special values of the real analytic GL2 Eisenstein series to the product of the Riemann zeta… (more)

Subjects/Keywords: Automorphic forms

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APA (6^th Edition):

Lim, L. (2013). Multiple Dirichlet Series Associated to Prehomogeneous Vector Spaces and the Relation with GL3(Z) Eisenstein Series. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:320644/

Chicago Manual of Style (16^th Edition):

Lim, Li-Mei. “Multiple Dirichlet Series Associated to Prehomogeneous Vector Spaces and the Relation with GL3(Z) Eisenstein Series.” 2013. Doctoral Dissertation, Brown University. Accessed March 07, 2021. https://repository.library.brown.edu/studio/item/bdr:320644/.

MLA Handbook (7^th Edition):

Lim, Li-Mei. “Multiple Dirichlet Series Associated to Prehomogeneous Vector Spaces and the Relation with GL3(Z) Eisenstein Series.” 2013. Web. 07 Mar 2021.

Vancouver:

Lim L. Multiple Dirichlet Series Associated to Prehomogeneous Vector Spaces and the Relation with GL3(Z) Eisenstein Series. [Internet] [Doctoral dissertation]. Brown University; 2013. [cited 2021 Mar 07]. Available from: https://repository.library.brown.edu/studio/item/bdr:320644/.

Council of Science Editors:

Lim L. Multiple Dirichlet Series Associated to Prehomogeneous Vector Spaces and the Relation with GL3(Z) Eisenstein Series. [Doctoral Dissertation]. Brown University; 2013. Available from: https://repository.library.brown.edu/studio/item/bdr:320644/

7. Bajpai, Jitendra K. On Vector-Valued Automorphic Forms.

Degree: PhD, Department of Mathematical and Statistical Sciences, 2015, University of Alberta

URL: https://era.library.ualberta.ca/files/chh63sv954

► Let \rG be a genus 0 Fuchsian group of the first kind\,, w ∈ 2\Z and ρ : \rG \longrightarrow \mr{GL}_d(\C) be any admissible representation… (more)

Subjects/Keywords: Automorphic Forms, Representation Theory; Fuchsian groups, Triangle groups; Vector-valued automorphic forms

…The Borcherds lift associates vvmf for a Weil representation to automorphic forms on… …developing the theory of vector-valued automorphic forms (vvaf) of Fuchsian groups. In… …valued theory of automorphic forms to vector-valued automorphic forms . This chapter is ended… …all . 2.2 Scalar-valued automorphic forms The basics of the theory of classical (i.e… …multiplier of the automorphic forms of G . This thesis mainly explore the theory of automorphic…

1 more image…

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APA (6^th Edition):

Bajpai, J. K. (2015). On Vector-Valued Automorphic Forms. (Doctoral Dissertation). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/chh63sv954

Chicago Manual of Style (16^th Edition):

Bajpai, Jitendra K. “On Vector-Valued Automorphic Forms.” 2015. Doctoral Dissertation, University of Alberta. Accessed March 07, 2021. https://era.library.ualberta.ca/files/chh63sv954.

MLA Handbook (7^th Edition):

Bajpai, Jitendra K. “On Vector-Valued Automorphic Forms.” 2015. Web. 07 Mar 2021.

Vancouver:

Bajpai JK. On Vector-Valued Automorphic Forms. [Internet] [Doctoral dissertation]. University of Alberta; 2015. [cited 2021 Mar 07]. Available from: https://era.library.ualberta.ca/files/chh63sv954.

Council of Science Editors:

Bajpai JK. On Vector-Valued Automorphic Forms. [Doctoral Dissertation]. University of Alberta; 2015. Available from: https://era.library.ualberta.ca/files/chh63sv954

University of Oklahoma

8. Shukla, Alok. On Klingen Eisenstein series with levels.

Degree: PhD, 2018, University of Oklahoma

URL: http://hdl.handle.net/11244/299326

► We give a representation theoretic approach to the Klingen lift generalizing the classical construction of Klingen Eisenstein series to arbitrary level for both paramodular and… (more)

Subjects/Keywords: Mathematics; Automorphic Representation; Klingen Eisenstein Series with levels; Paramodular; Co-dimension formula for cusp forms

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APA (6^th Edition):

Shukla, A. (2018). On Klingen Eisenstein series with levels. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/299326

Chicago Manual of Style (16^th Edition):

Shukla, Alok. “On Klingen Eisenstein series with levels.” 2018. Doctoral Dissertation, University of Oklahoma. Accessed March 07, 2021. http://hdl.handle.net/11244/299326.

MLA Handbook (7^th Edition):

Shukla, Alok. “On Klingen Eisenstein series with levels.” 2018. Web. 07 Mar 2021.

Vancouver:

Shukla A. On Klingen Eisenstein series with levels. [Internet] [Doctoral dissertation]. University of Oklahoma; 2018. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/11244/299326.

Council of Science Editors:

Shukla A. On Klingen Eisenstein series with levels. [Doctoral Dissertation]. University of Oklahoma; 2018. Available from: http://hdl.handle.net/11244/299326

9. Moore, Daniel Ross. An Intrinsic Theory of Smooth Automorphic Representations.

Degree: PhD, Mathematics, 2018, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1524174589105537

► Our goal in this paper is to lay the foundation for a theory of smooth automorphic forms and representations on local and adelic reductive groups… (more)

▼ Our goal in this paper is to lay the foundation for a theory of smooth automorphic forms and representations on local and adelic reductive groups G that does not rely on the K-finite or classical unitary theories. Specifically, we consider forms that are smooth but not necessarily K-finite, that is, whose orbits under a maximal compact subgroup are not necessarily contained in finite dimensional spaces. To do so, we introduce spaces of automorphic forms of "fixed type" à la Borel and Jacquet, imposing locally convex topologies to gain control of these now infinite dimensional spaces. Along the way we present a novel treatment of group norms on G, emphasizing their compatibility both with the structure of G as a reductive group and a restricted product of reductive groups over local fields.Motivated by the work of Wallach in the 1980s, we relate the asymptotic behavior of our representations to the growth of the automorphic forms that generate them. We show that our smooth representations behave analogously to the Casselman-Wallach globalizations of representations of real reductive groups. We then introduce a new algebra of "Schwartz functions" on G and demonstrate it serves the same role for smooth representations as the Hecke algebra does for their K-finite counterparts.Ultimately, our aim is to illustrate how smooth representations serve the same role for K-finite automorphic representations as Casselman-Wallach globalizations do for Harish-Chandra modules. Our tensor product theorem for smooth automorphic representations completes the picture of these representations as generalizations of Casselman-Wallach globalizations. Therein we show the "factors" of such a representation (ϖ, V) at the archimedean places are precisely the Casselman-Wallach globalizations corresponding to archimedean factors in the underlying Harish-Chandra module of K-finite vectors in V. Advisors/Committee Members: Cogdell, James (Advisor).

Subjects/Keywords: Mathematics; analytic number theory; automorphic representation theory; Schwartz functions; Casselman-Wallach

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APA (6^th Edition):

Moore, D. R. (2018). An Intrinsic Theory of Smooth Automorphic Representations. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1524174589105537

Chicago Manual of Style (16^th Edition):

Moore, Daniel Ross. “An Intrinsic Theory of Smooth Automorphic Representations.” 2018. Doctoral Dissertation, The Ohio State University. Accessed March 07, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524174589105537.

MLA Handbook (7^th Edition):

Moore, Daniel Ross. “An Intrinsic Theory of Smooth Automorphic Representations.” 2018. Web. 07 Mar 2021.

Vancouver:

Moore DR. An Intrinsic Theory of Smooth Automorphic Representations. [Internet] [Doctoral dissertation]. The Ohio State University; 2018. [cited 2021 Mar 07]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1524174589105537.

Council of Science Editors:

Moore DR. An Intrinsic Theory of Smooth Automorphic Representations. [Doctoral Dissertation]. The Ohio State University; 2018. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1524174589105537

University of Ottawa

10. Saber, Hicham. Vector-valued Automorphic Forms and Vector Bundles .

Degree: 2015, University of Ottawa

URL: http://hdl.handle.net/10393/33136

► In this thesis we prove the existence of vector-valued automorphic forms for an arbitrary Fuchsian group and an arbitrary finite dimensional complex representation of this… (more)

Subjects/Keywords: Automorphic Forms; Vector Bundles

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APA (6^th Edition):

Saber, H. (2015). Vector-valued Automorphic Forms and Vector Bundles . (Thesis). University of Ottawa. Retrieved from http://hdl.handle.net/10393/33136

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Saber, Hicham. “Vector-valued Automorphic Forms and Vector Bundles .” 2015. Thesis, University of Ottawa. Accessed March 07, 2021. http://hdl.handle.net/10393/33136.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Saber, Hicham. “Vector-valued Automorphic Forms and Vector Bundles .” 2015. Web. 07 Mar 2021.

Vancouver:

Saber H. Vector-valued Automorphic Forms and Vector Bundles . [Internet] [Thesis]. University of Ottawa; 2015. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/10393/33136.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Saber H. Vector-valued Automorphic Forms and Vector Bundles . [Thesis]. University of Ottawa; 2015. Available from: http://hdl.handle.net/10393/33136

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

11. Balkanova, Olga. The fourth moment of automorphic L-functions at prime power level : Le quatrième moment de fonctions L automorphes de niveau une grande puissance d'un nombre premier.

Degree: Docteur es, Mathematiques pures, 2015, Bordeaux; Università degli studi (Milan, Italie)

URL: http://www.theses.fr/2015BORD0053

►

Le résultat principal de cette thèse est une formule asymptotique pour le quatrième moment des fonctions L automorphes de niveau p', où p est un… (more)

Subjects/Keywords: Fonctions L; Formes automorphes; Théorie des matrices aléatoires; L functions; Automorphic forms; Random matrix theory

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APA (6^th Edition):

Balkanova, O. (2015). The fourth moment of automorphic L-functions at prime power level : Le quatrième moment de fonctions L automorphes de niveau une grande puissance d'un nombre premier. (Doctoral Dissertation). Bordeaux; Università degli studi (Milan, Italie). Retrieved from http://www.theses.fr/2015BORD0053

Chicago Manual of Style (16^th Edition):

Balkanova, Olga. “The fourth moment of automorphic L-functions at prime power level : Le quatrième moment de fonctions L automorphes de niveau une grande puissance d'un nombre premier.” 2015. Doctoral Dissertation, Bordeaux; Università degli studi (Milan, Italie). Accessed March 07, 2021. http://www.theses.fr/2015BORD0053.

MLA Handbook (7^th Edition):

Balkanova, Olga. “The fourth moment of automorphic L-functions at prime power level : Le quatrième moment de fonctions L automorphes de niveau une grande puissance d'un nombre premier.” 2015. Web. 07 Mar 2021.

Vancouver:

Balkanova O. The fourth moment of automorphic L-functions at prime power level : Le quatrième moment de fonctions L automorphes de niveau une grande puissance d'un nombre premier. [Internet] [Doctoral dissertation]. Bordeaux; Università degli studi (Milan, Italie); 2015. [cited 2021 Mar 07]. Available from: http://www.theses.fr/2015BORD0053.

Council of Science Editors:

Balkanova O. The fourth moment of automorphic L-functions at prime power level : Le quatrième moment de fonctions L automorphes de niveau une grande puissance d'un nombre premier. [Doctoral Dissertation]. Bordeaux; Università degli studi (Milan, Italie); 2015. Available from: http://www.theses.fr/2015BORD0053

12. Robinson, Christine A. On Siegel Maass Wave Forms of Weight 0.

Degree: 2013, University of Illinois – Chicago

URL: http://hdl.handle.net/10027/9982

► Progress has been made toward a Saito-Kurokawa lift, including a non-holomorphic Shimura lift and a lift from the non-holomorphic analogue of the Kohnen plus space… (more)

▼ Progress has been made toward a Saito-Kurokawa lift, including a non-holomorphic Shimura lift and a lift from the non-holomorphic analogue of the Kohnen plus space to Jacobi Maass forms. A large gap remains in our understanding of Siegel Maass forms, which are the non-holomorphic analogue of Siegel modular forms. Relatively few results are known with a high degree of generality, and even basic results have not been developed in some cases. In the case of Siegel Maass wave forms of weight 0, Niwa, in 1991, utilized explicit differential operators given by Nakajima (1982) to develop the Fourier series expansion. However, Nakajima's quartic differential operator is not invariant under the action of the desired slash operator, and so we still lack a valid Fourier expansion for Siegel Maass wave forms of weight 0. In this thesis, we introduce Siegel Maass wave forms of weight 0, which are simultaneous eigenvectors of Maass' Casimir operators, rather than the operators given by Nakajima, and follow the method of Niwa to obtain a fourth order ordinary differential equation, which must be satisfied by the Fourier coefficients of such wave forms. In Chapter 2, we review the theory of holomorphic Siegel modular forms and the classical Saito-Kurokawa lift. In Section 3.1, we define Siegel Maass wave forms of weight 0, and in Section 3.2, we describe non-holomorphic automorphic forms involved in a Saito-Kurokawa lift, as well as the maps between them which have previously been established. In Section 4.1, we explicitly compute the Casimir operators which form the basis for our definition of Siegel Maass wave forms, followed by the computation of the system of differential equations satisfied by these forms, in Section 4.2. In Section 4.3, through a series of changes of variable, we reduce this system of differential equations to a single fourth order ordinary linear differential equation. The Fourier coefficient of a wave form, corresponding to the identity matrix, will satisfy this differential equation. We discuss the proof given by Niwa for the solutions to his ordinary differential equation and his method for obtaining the first solution by theta lifting, in Section 4.4, and finally we conclude in Section 4.5 by giving the Fourier coefficients corresponding to definite matrices, according to Hori. Advisors/Committee Members: Takloo-Bighash, Ramin (advisor), Hurder, Steven (committee member), Radford, David (committee member), Shipley, Brooke (committee member), Marshall, Simon (committee member).

Subjects/Keywords: number theory; automorphic forms; Siegel modular forms

…attempts at a theory of non-holomorphic Jacobi Maass forms, and establishes a correspondence… …HOLOMORPHIC THEORY 2.1 Siegel modular forms What we now call Siegel modular forms were developed… …kinds of automorphic forms in several complex variables. Various “lifting” theorems have been… …a similarly important role in the theory of Siegel modular forms. Let G = GSp(2g, Q… …of the Langlands automorphic L-function, corresponding to the spinor representation of the…

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APA (6^th Edition):

Robinson, C. A. (2013). On Siegel Maass Wave Forms of Weight 0. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/9982

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Robinson, Christine A. “On Siegel Maass Wave Forms of Weight 0.” 2013. Thesis, University of Illinois – Chicago. Accessed March 07, 2021. http://hdl.handle.net/10027/9982.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Robinson, Christine A. “On Siegel Maass Wave Forms of Weight 0.” 2013. Web. 07 Mar 2021.

Vancouver:

Robinson CA. On Siegel Maass Wave Forms of Weight 0. [Internet] [Thesis]. University of Illinois – Chicago; 2013. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/10027/9982.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Robinson CA. On Siegel Maass Wave Forms of Weight 0. [Thesis]. University of Illinois – Chicago; 2013. Available from: http://hdl.handle.net/10027/9982

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Minnesota

13. Sands, Adrienne. Automorphic Hamiltonians, Epstein zeta functions, and Kronecker limit formulas.

Degree: PhD, Mathematics, 2020, University of Minnesota

URL: http://hdl.handle.net/11299/217155

We construct an automorphic Hamiltonian which has purely discrete spectrum on L² ≤ ft(SL_r(\Z)\backslash SL_r(\R)/SO(r,\R))), identify its ground state, and show how it can characterize a nuclear Fr\'echet automorphic Schwartz space.

Subjects/Keywords: Automorphic forms; Automorphic Hamiltonian; Automorphic Schwartz space; Degenerate Eisenstein series; Epstein zeta functions

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APA (6^th Edition):

Sands, A. (2020). Automorphic Hamiltonians, Epstein zeta functions, and Kronecker limit formulas. (Doctoral Dissertation). University of Minnesota. Retrieved from http://hdl.handle.net/11299/217155

Chicago Manual of Style (16^th Edition):

Sands, Adrienne. “Automorphic Hamiltonians, Epstein zeta functions, and Kronecker limit formulas.” 2020. Doctoral Dissertation, University of Minnesota. Accessed March 07, 2021. http://hdl.handle.net/11299/217155.

MLA Handbook (7^th Edition):

Sands, Adrienne. “Automorphic Hamiltonians, Epstein zeta functions, and Kronecker limit formulas.” 2020. Web. 07 Mar 2021.

Vancouver:

Sands A. Automorphic Hamiltonians, Epstein zeta functions, and Kronecker limit formulas. [Internet] [Doctoral dissertation]. University of Minnesota; 2020. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/11299/217155.

Council of Science Editors:

Sands A. Automorphic Hamiltonians, Epstein zeta functions, and Kronecker limit formulas. [Doctoral Dissertation]. University of Minnesota; 2020. Available from: http://hdl.handle.net/11299/217155

14. Allen, Patrick. Modularity of nearly ordinary 2-adic residually dihedral Galois representations.

Degree: Mathematics, 2012, UCLA

URL: http://www.escholarship.org/uc/item/1nk3w1xd

► We prove modularity of some two dimensional 2-adic Galois representations over a totally real field that are nearly ordinary at all places above 2 and… (more)

Subjects/Keywords: Mathematics; Automorphic forms; Galois representations; Number theory

…automorphic forms, are what is known as modularity lifting theorems. Given a Galois representation… …between Galois representations and automorphic forms. Galois representations arise quite… …deduce properties of the geometric object. Automorphic forms are certain complex analytic… …modular forms. A priori, automorphic forms and Galois representations don’t appear to have… …analysis. The idea that arithmetic objects should have automorphic forms associated to them was…

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APA (6^th Edition):

Allen, P. (2012). Modularity of nearly ordinary 2-adic residually dihedral Galois representations. (Thesis). UCLA. Retrieved from http://www.escholarship.org/uc/item/1nk3w1xd

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Allen, Patrick. “Modularity of nearly ordinary 2-adic residually dihedral Galois representations.” 2012. Thesis, UCLA. Accessed March 07, 2021. http://www.escholarship.org/uc/item/1nk3w1xd.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Allen, Patrick. “Modularity of nearly ordinary 2-adic residually dihedral Galois representations.” 2012. Web. 07 Mar 2021.

Vancouver:

Allen P. Modularity of nearly ordinary 2-adic residually dihedral Galois representations. [Internet] [Thesis]. UCLA; 2012. [cited 2021 Mar 07]. Available from: http://www.escholarship.org/uc/item/1nk3w1xd.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Allen P. Modularity of nearly ordinary 2-adic residually dihedral Galois representations. [Thesis]. UCLA; 2012. Available from: http://www.escholarship.org/uc/item/1nk3w1xd

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Cambridge

15. Chen, Cangxiong. ON ASAI’S FUNCTION ANALOGOUS TO log |η(z)|.

Degree: PhD, 2015, University of Cambridge

URL: https://www.repository.cam.ac.uk/handle/1810/306109https://www.repository.cam.ac.uk/bitstream/1810/306109/2/license.txt

► Kronecker’s first limit formula describes the constant term in the Laurent expansion of a non-holomorphic Eisenstein series at one of its poles. Asai generalised the… (more)

Subjects/Keywords: Algebraic number theory; Automorphic forms; Asai's function; Eisenstein series; Kronecker Limit Formula; L-functions; Rankin-Selberg integral

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APA (6^th Edition):

Chen, C. (2015). ON ASAI’S FUNCTION ANALOGOUS TO log |η(z)|. (Doctoral Dissertation). University of Cambridge. Retrieved from https://www.repository.cam.ac.uk/handle/1810/306109https://www.repository.cam.ac.uk/bitstream/1810/306109/2/license.txt

Chicago Manual of Style (16^th Edition):

Chen, Cangxiong. “ON ASAI’S FUNCTION ANALOGOUS TO log |η(z)|.” 2015. Doctoral Dissertation, University of Cambridge. Accessed March 07, 2021. https://www.repository.cam.ac.uk/handle/1810/306109https://www.repository.cam.ac.uk/bitstream/1810/306109/2/license.txt.

MLA Handbook (7^th Edition):

Chen, Cangxiong. “ON ASAI’S FUNCTION ANALOGOUS TO log |η(z)|.” 2015. Web. 07 Mar 2021.

Vancouver:

Chen C. ON ASAI’S FUNCTION ANALOGOUS TO log |η(z)|. [Internet] [Doctoral dissertation]. University of Cambridge; 2015. [cited 2021 Mar 07]. Available from: https://www.repository.cam.ac.uk/handle/1810/306109https://www.repository.cam.ac.uk/bitstream/1810/306109/2/license.txt.

Council of Science Editors:

Chen C. ON ASAI’S FUNCTION ANALOGOUS TO log |η(z)|. [Doctoral Dissertation]. University of Cambridge; 2015. Available from: https://www.repository.cam.ac.uk/handle/1810/306109https://www.repository.cam.ac.uk/bitstream/1810/306109/2/license.txt

16. Jung, Junehyuk. On the zeros of automorphic forms .

Degree: PhD, 2013, Princeton University

URL: http://arks.princeton.edu/ark:/88435/dsp01fx719m52n

► The subject of this thesis is the zeros of automorphic forms. In the first part, we study the asymptotic behavior of nodal lines of Maass… (more)

Subjects/Keywords: Automorphic forms; Number theory; Spectral geometry

…77 8.2 Dihedral forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78… …B if A = B + o(B) as B → ∞. 1 Part I Nodal lines of Maass cusp forms 2… …x28;T 5/6+ ) forms within the set of even Maass-Hecke cusp forms in {φ | T < τφ… …are ∼ T /24 even Maass-Hecke cusp forms in {φ | T < τφ < T + 1}. The assumption of… …fixed geodesic segment β ⊂ δ, all but O (T 1/3+ ) forms within the set of even Maass…

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APA (6^th Edition):

Jung, J. (2013). On the zeros of automorphic forms . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp01fx719m52n

Chicago Manual of Style (16^th Edition):

Jung, Junehyuk. “On the zeros of automorphic forms .” 2013. Doctoral Dissertation, Princeton University. Accessed March 07, 2021. http://arks.princeton.edu/ark:/88435/dsp01fx719m52n.

MLA Handbook (7^th Edition):

Jung, Junehyuk. “On the zeros of automorphic forms .” 2013. Web. 07 Mar 2021.

Vancouver:

Jung J. On the zeros of automorphic forms . [Internet] [Doctoral dissertation]. Princeton University; 2013. [cited 2021 Mar 07]. Available from: http://arks.princeton.edu/ark:/88435/dsp01fx719m52n.

Council of Science Editors:

Jung J. On the zeros of automorphic forms . [Doctoral Dissertation]. Princeton University; 2013. Available from: http://arks.princeton.edu/ark:/88435/dsp01fx719m52n

University of Cambridge

17. Chen, Cangxiong. On Asai's function analogous to log |η(z)|.

Degree: PhD, 2015, University of Cambridge

URL: https://doi.org/10.17863/CAM.53187 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.809989

► Kronecker’s first limit formula describes the constant term in the Laurent expansion of a non-holomorphic Eisenstein series at one of its poles. Asai generalised the… (more)

Subjects/Keywords: Algebraic number theory; Automorphic forms; Asai's function; Eisenstein series; Kronecker Limit Formula; L-functions; Rankin-Selberg integral

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Chen, C. (2015). On Asai's function analogous to log |η(z)|. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.53187 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.809989

Chicago Manual of Style (16^th Edition):

Chen, Cangxiong. “On Asai's function analogous to log |η(z)|.” 2015. Doctoral Dissertation, University of Cambridge. Accessed March 07, 2021. https://doi.org/10.17863/CAM.53187 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.809989.

MLA Handbook (7^th Edition):

Chen, Cangxiong. “On Asai's function analogous to log |η(z)|.” 2015. Web. 07 Mar 2021.

Vancouver:

Chen C. On Asai's function analogous to log |η(z)|. [Internet] [Doctoral dissertation]. University of Cambridge; 2015. [cited 2021 Mar 07]. Available from: https://doi.org/10.17863/CAM.53187 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.809989.

Council of Science Editors:

Chen C. On Asai's function analogous to log |η(z)|. [Doctoral Dissertation]. University of Cambridge; 2015. Available from: https://doi.org/10.17863/CAM.53187 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.809989

Princeton University

18. Su, Jun. Coherent cohomology of Shimura varieties and automorphic forms .

Degree: PhD, 2019, Princeton University

URL: http://arks.princeton.edu/ark:/88435/dsp010p096979s

► In this thesis, we show that the cohomology of canonical extensions of automorphic vector bundles over toroidal compactifications of Shimura varieties can be computed by… (more)

Subjects/Keywords: automorphic forms; automorphic vector bundles; Shimura varieties; toroidal compactifications

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Su, J. (2019). Coherent cohomology of Shimura varieties and automorphic forms . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp010p096979s

Chicago Manual of Style (16^th Edition):

Su, Jun. “Coherent cohomology of Shimura varieties and automorphic forms .” 2019. Doctoral Dissertation, Princeton University. Accessed March 07, 2021. http://arks.princeton.edu/ark:/88435/dsp010p096979s.

MLA Handbook (7^th Edition):

Su, Jun. “Coherent cohomology of Shimura varieties and automorphic forms .” 2019. Web. 07 Mar 2021.

Vancouver:

Su J. Coherent cohomology of Shimura varieties and automorphic forms . [Internet] [Doctoral dissertation]. Princeton University; 2019. [cited 2021 Mar 07]. Available from: http://arks.princeton.edu/ark:/88435/dsp010p096979s.

Council of Science Editors:

Su J. Coherent cohomology of Shimura varieties and automorphic forms . [Doctoral Dissertation]. Princeton University; 2019. Available from: http://arks.princeton.edu/ark:/88435/dsp010p096979s

University of Ottawa

19. Mousaaid, Youssef. Convers Theorems of Borcherds Products .

Degree: 2018, University of Ottawa

URL: http://hdl.handle.net/10393/38405

► In his paper, Borcherds introduced a theta lift which allowed him to lift classical modular forms with poles at cusps to automorphic forms on the… (more)

Subjects/Keywords: Borcherds products; Heegner divisors; Automorphic forms

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APA (6^th Edition):

Mousaaid, Y. (2018). Convers Theorems of Borcherds Products . (Thesis). University of Ottawa. Retrieved from http://hdl.handle.net/10393/38405

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Mousaaid, Youssef. “Convers Theorems of Borcherds Products .” 2018. Thesis, University of Ottawa. Accessed March 07, 2021. http://hdl.handle.net/10393/38405.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Mousaaid, Youssef. “Convers Theorems of Borcherds Products .” 2018. Web. 07 Mar 2021.

Vancouver:

Mousaaid Y. Convers Theorems of Borcherds Products . [Internet] [Thesis]. University of Ottawa; 2018. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/10393/38405.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Mousaaid Y. Convers Theorems of Borcherds Products . [Thesis]. University of Ottawa; 2018. Available from: http://hdl.handle.net/10393/38405

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Melbourne

20. McAndrew, Angus William. Galois representations and theta operators for Siegel modular forms.

Degree: 2015, University of Melbourne

URL: http://hdl.handle.net/11343/57014

► Modular forms are powerful number theoretic objects, having attracted much study and attention for the last 200 years. In the modern area, one of their… (more)

Subjects/Keywords: number theory; representation theory; algebraic geometry; Galois representations; modular forms; Siegel modular forms; Serre's conjecture

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APA (6^th Edition):

McAndrew, A. W. (2015). Galois representations and theta operators for Siegel modular forms. (Masters Thesis). University of Melbourne. Retrieved from http://hdl.handle.net/11343/57014

Chicago Manual of Style (16^th Edition):

McAndrew, Angus William. “Galois representations and theta operators for Siegel modular forms.” 2015. Masters Thesis, University of Melbourne. Accessed March 07, 2021. http://hdl.handle.net/11343/57014.

MLA Handbook (7^th Edition):

McAndrew, Angus William. “Galois representations and theta operators for Siegel modular forms.” 2015. Web. 07 Mar 2021.

Vancouver:

McAndrew AW. Galois representations and theta operators for Siegel modular forms. [Internet] [Masters thesis]. University of Melbourne; 2015. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/11343/57014.

Council of Science Editors:

McAndrew AW. Galois representations and theta operators for Siegel modular forms. [Masters Thesis]. University of Melbourne; 2015. Available from: http://hdl.handle.net/11343/57014

21. Alluhaibi, Nadia. On vector-valued automorphic forms on bounded symmetric domains.

Degree: 2017, University of Western Ontario

URL: https://ir.lib.uwo.ca/etd/4498

► The objective of the study is to investigate the behaviour of the inner products of vector-valued Poincare series, for large weight, associated to submanifolds of… (more)

Subjects/Keywords: automorphic forms; asymptotics; poincare series; bounded domains; modular forms; bergman kernel; hyperbolic space; Algebraic Geometry; Analysis; Geometry and Topology; Number Theory; Physical Sciences and Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Alluhaibi, N. (2017). On vector-valued automorphic forms on bounded symmetric domains. (Thesis). University of Western Ontario. Retrieved from https://ir.lib.uwo.ca/etd/4498

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Alluhaibi, Nadia. “On vector-valued automorphic forms on bounded symmetric domains.” 2017. Thesis, University of Western Ontario. Accessed March 07, 2021. https://ir.lib.uwo.ca/etd/4498.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Alluhaibi, Nadia. “On vector-valued automorphic forms on bounded symmetric domains.” 2017. Web. 07 Mar 2021.

Vancouver:

Alluhaibi N. On vector-valued automorphic forms on bounded symmetric domains. [Internet] [Thesis]. University of Western Ontario; 2017. [cited 2021 Mar 07]. Available from: https://ir.lib.uwo.ca/etd/4498.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Alluhaibi N. On vector-valued automorphic forms on bounded symmetric domains. [Thesis]. University of Western Ontario; 2017. Available from: https://ir.lib.uwo.ca/etd/4498

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Hong Kong

22. Fung, King-cheong. Modular forms of small weight and their applications.

Degree: 2017, University of Hong Kong

URL: http://hdl.handle.net/10722/249204

► In number theory, as well as many areas in mathematics, modular forms (or in general, automorphic forms) are powerful tools which have many applications. In… (more)

▼ In number theory, as well as many areas in mathematics, modular forms (or in general, automorphic forms) are powerful tools which have many applications. In this thesis, the author focuses on modular forms of small weight and their applications. The author is particularly inter- ested in weight 3=2 and 2. In fact, cusp forms of weight 3=2 and cusp forms of weight 2 are closely linked together by the well-known Shimura correspondences. In general, many properties of half-integral weight cusp forms were exploited from the properties of integral weight cusp forms through the Shimura correspondence. Chapter 1 is an introduction where denitions and preliminaries are provided. Chapter 2 deals with dierent altered weight 2 Eisenstein series for the full modular group. Chapter 3 deals with a weight 3=2 cusp forms which has an application of proving the halting of an algorithm which computes a supersingular elliptic curve with a given endormorphism ring. In Chapter 2, the author reviews a technique of Hecke and give an analytic continuation of an altered Eisenstein series G(z; s) := X m;n 0 1 (mz + n)2jmz + njs on the complex s-plane with <(s) > 􀀀1. Then, the author considers a holomorphic series G(z; s) := X m;n 0 1 (mz + n)2+s and let s approach 0 along the real line. The author is interested in whether the holomorphic property for z or the modularity of it is lost. After that, a multiplier system introduced by Petersson is briey in- troduced. The author reviews that the modularity of G(z; s) attached with Petersson's MS is obtained and it is expected to have 0 when s ap- proaches 0. A comparison of the modularity and holomorphicity of the three altered series when s = 0 is made at the end of Chapter 2. In Chapter 3, the author rst gives a background of problems concern- ing the endomorphism ring of an elliptic curve and describe the algorithm by Chevyrev and Galbraith which provides applications in algorithmic theory of elliptic curves over nite elds. Then, the author gives a precise statement of a conjecture by Chevyrev and Galbraith which ensures the halting of their algorithm. After that, a detailed proof of the conjecture is given. An equivalence among isomorphicity of a pair of maximal orders, agreement of a pair of theta series associated with the pair of maximal orders, and the global equivalency of their associated quadratic forms are given. At the end, the author describes the second conjecture of Chevyrev and Galbraith which are used to nd the running time of their algorithm and give some suggestions on further research in this topic. Advisors/Committee Members: Kane, BR (advisor), Lau, YK (advisor).

Subjects/Keywords: Automorphic forms; Forms, Modular

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Fung, K. (2017). Modular forms of small weight and their applications. (Thesis). University of Hong Kong. Retrieved from http://hdl.handle.net/10722/249204

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Fung, King-cheong. “Modular forms of small weight and their applications.” 2017. Thesis, University of Hong Kong. Accessed March 07, 2021. http://hdl.handle.net/10722/249204.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Fung, King-cheong. “Modular forms of small weight and their applications.” 2017. Web. 07 Mar 2021.

Vancouver:

Fung K. Modular forms of small weight and their applications. [Internet] [Thesis]. University of Hong Kong; 2017. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/10722/249204.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Fung K. Modular forms of small weight and their applications. [Thesis]. University of Hong Kong; 2017. Available from: http://hdl.handle.net/10722/249204

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

23. Nguyen, Manh Tu. Higher Hida Theory on Unitary Group GU (2,1) : Théorie de Hida supérieur pour le groupe unitaire GU (2,1).

Degree: Docteur es, Mathématiques, 2020, Lyon

URL: http://www.theses.fr/2020LYSEN009

►

Le travaux récent de Calegari et Geraghty ont enlevé les restrictions de la méthode originale de Taylor-Wiles, cela nous permet d’attaquer les conjectures de modularité… (more)

▼

Le travaux récent de Calegari et Geraghty ont enlevé les restrictions de la méthode originale de Taylor-Wiles, cela nous permet d’attaquer les conjectures de modularité plus générales. Leur méthode se fonde sur deux autres conjectures, l'une est reliée au problème d'attacher les représentations galoisiennes aux classes de torsion dans le groupe de cohomologie de la variété de Shimura sous entendue et l'autre à la dégrée de concentration de ces groupes de cohomologie localisés. La première conjecture a été adressée dans une grande généralité par Peter Scholze mais la seconde reste évasive. Récemment, pour la cohomologie cohérente, Vincent Pilloni a développé une version de la théorie de Hida pour les groupes de cohomologie supérieurs qui construit une interpolation p-adique du complexe de cohomologie en question. Comme une application importante, nous pouvons contourner la second conjecture au dessus et en effet dans un travail commun récent, Vincent Pilloni avec ses collaborateurs ont montré que toutes les variétés abéliennes sur un corps totalement réel est potentiellement modulaire. Dans cette thèse, nous adaptons l'argument de Vincent Pilloni pour construire un complexe qui interpole les classes de cohomologie supérieurs de la variété de Picard. Ces résultats servent comme le premier pas vers la modularité potentielle des variétés abéliennes de dimension 3 qui proviennent des Jacobiens de la courbe de Picard.

In their breakthrough work, Calegari and Geraghty have shown how to bypass some serious restrictions of the original method by Taylor-Wiles, thus allowing us to attack more general modularity conjectures and related questions. Their method hinges on two conjectures, one is related to the problem of attaching Galois representations to torsion classes in the cohomology of Shimura varieties and the other to the requirement that these cohomology groups, localised at an appropriate ideal are non zero only in a certain range. The first conjecture is addressed in a great generality by Peter Scholze, but the second remains elusive. Recently, for coherent cohomology, inspired by the classical Hida theory, Vincent Pilloni has proposed a method consisting of p-adically interpolating the entire complex of coherent sheaves of automorphic forms on the Siegel threefold. This serves as a way to get around the second conjecture above and plays a crucial role in a recent work, where they show that abelian surfaces over a totally real field are potentially modular. In this thesis, we adapt the argument of Pilloni to construct a Hida complex interpolating classes in higher cohomology groups of the Picard modular surface. In a future work, we hope to use this to obtain some similar modularity results for abelian three-folds arising as Jacobians of some Picard curves.

Advisors/Committee Members: Pilloni, Vincent (thesis director).

Subjects/Keywords: Variété de Shimura; Forme automorphe p-adique; Modularité; Overconvergent automorphic forms; Shimura variety; P-adic automorphic forms; Modularity; Overconvergent forms

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Nguyen, M. T. (2020). Higher Hida Theory on Unitary Group GU (2,1) : Théorie de Hida supérieur pour le groupe unitaire GU (2,1). (Doctoral Dissertation). Lyon. Retrieved from http://www.theses.fr/2020LYSEN009

Chicago Manual of Style (16^th Edition):

Nguyen, Manh Tu. “Higher Hida Theory on Unitary Group GU (2,1) : Théorie de Hida supérieur pour le groupe unitaire GU (2,1).” 2020. Doctoral Dissertation, Lyon. Accessed March 07, 2021. http://www.theses.fr/2020LYSEN009.

MLA Handbook (7^th Edition):

Nguyen, Manh Tu. “Higher Hida Theory on Unitary Group GU (2,1) : Théorie de Hida supérieur pour le groupe unitaire GU (2,1).” 2020. Web. 07 Mar 2021.

Vancouver:

Nguyen MT. Higher Hida Theory on Unitary Group GU (2,1) : Théorie de Hida supérieur pour le groupe unitaire GU (2,1). [Internet] [Doctoral dissertation]. Lyon; 2020. [cited 2021 Mar 07]. Available from: http://www.theses.fr/2020LYSEN009.

Council of Science Editors:

Nguyen MT. Higher Hida Theory on Unitary Group GU (2,1) : Théorie de Hida supérieur pour le groupe unitaire GU (2,1). [Doctoral Dissertation]. Lyon; 2020. Available from: http://www.theses.fr/2020LYSEN009

University of Hong Kong

24. 徐晨. On a mean value of twisted automorphic L-functions.

Degree: 2008, University of Hong Kong

URL: http://hdl.handle.net/10722/51868

Subjects/Keywords: L-functions.; Automorphic forms.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

徐晨. (2008). On a mean value of twisted automorphic L-functions. (Thesis). University of Hong Kong. Retrieved from http://hdl.handle.net/10722/51868

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

徐晨. “On a mean value of twisted automorphic L-functions.” 2008. Thesis, University of Hong Kong. Accessed March 07, 2021. http://hdl.handle.net/10722/51868.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

徐晨. “On a mean value of twisted automorphic L-functions.” 2008. Web. 07 Mar 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

徐晨. On a mean value of twisted automorphic L-functions. [Internet] [Thesis]. University of Hong Kong; 2008. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/10722/51868.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

徐晨. On a mean value of twisted automorphic L-functions. [Thesis]. University of Hong Kong; 2008. Available from: http://hdl.handle.net/10722/51868

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation

Princeton University

25. Varma, Ila. On local-global compatibility for cuspidal regular algebraic automorphic representations of GLn .

Degree: PhD, 2015, Princeton University

URL: http://arks.princeton.edu/ark:/88435/dsp01g158bk68k

► We prove the compatibility of local and global Langlands correspondences for \GL_n up to semisimplification for the Galois representations constructed by Harris-Lan-Taylor-Thorne and Scholze. More… (more)

Subjects/Keywords: Galois representations; Langlands program; p-adic automorphic forms

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APA (6^th Edition):

Varma, I. (2015). On local-global compatibility for cuspidal regular algebraic automorphic representations of GLn . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp01g158bk68k

Chicago Manual of Style (16^th Edition):

Varma, Ila. “On local-global compatibility for cuspidal regular algebraic automorphic representations of GLn .” 2015. Doctoral Dissertation, Princeton University. Accessed March 07, 2021. http://arks.princeton.edu/ark:/88435/dsp01g158bk68k.

MLA Handbook (7^th Edition):

Varma, Ila. “On local-global compatibility for cuspidal regular algebraic automorphic representations of GLn .” 2015. Web. 07 Mar 2021.

Vancouver:

Varma I. On local-global compatibility for cuspidal regular algebraic automorphic representations of GLn . [Internet] [Doctoral dissertation]. Princeton University; 2015. [cited 2021 Mar 07]. Available from: http://arks.princeton.edu/ark:/88435/dsp01g158bk68k.

Council of Science Editors:

Varma I. On local-global compatibility for cuspidal regular algebraic automorphic representations of GLn . [Doctoral Dissertation]. Princeton University; 2015. Available from: http://arks.princeton.edu/ark:/88435/dsp01g158bk68k

The Ohio State University

26. Brewster, Stephen Thomas. Automorphisms of the cohomology ring of finite Grassmann manifolds.

Degree: PhD, Graduate School, 1978, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1487082492038354

Subjects/Keywords: Mathematics; Automorphic forms; Manifolds

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APA (6^th Edition):

Brewster, S. T. (1978). Automorphisms of the cohomology ring of finite Grassmann manifolds. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1487082492038354

Chicago Manual of Style (16^th Edition):

Brewster, Stephen Thomas. “Automorphisms of the cohomology ring of finite Grassmann manifolds.” 1978. Doctoral Dissertation, The Ohio State University. Accessed March 07, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487082492038354.

MLA Handbook (7^th Edition):

Brewster, Stephen Thomas. “Automorphisms of the cohomology ring of finite Grassmann manifolds.” 1978. Web. 07 Mar 2021.

Vancouver:

Brewster ST. Automorphisms of the cohomology ring of finite Grassmann manifolds. [Internet] [Doctoral dissertation]. The Ohio State University; 1978. [cited 2021 Mar 07]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1487082492038354.

Council of Science Editors:

Brewster ST. Automorphisms of the cohomology ring of finite Grassmann manifolds. [Doctoral Dissertation]. The Ohio State University; 1978. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1487082492038354

27. Savala, Paul. Computing spectral data for Maass cusp forms using resonance.

Degree: PhD, Mathematics, 2016, University of Iowa

URL: https://ir.uiowa.edu/etd/3182

► The primary arithmetic information attached to a Maass cusp form is its Laplace eigenvalue. However, in the case of cuspidal Maass forms, the range… (more)

Subjects/Keywords: publicabstract; automorphic forms; laplace eigenvalue; maass forms; number theory; resonance; Mathematics

…Maass forms show up in the larger theory. A Maass form can be lifted to an automorphic… …1 2 2 5 6 2 COMPUTATION OF AUTOMORPHIC FORMS . . . . . . . . . . . . 11 1.4 2.1 2.2… …2.3 2.4 2.5 Automorphic Forms and the Riemann Zeta Function Modular Forms… …55 viii 1 CHAPTER 1 INTRODUCTION AND BACKGROUND 1.1 Automorphic Forms and the Riemann… …the same key properties. These functions are known as “automorphic forms.” 2 1.2 Modular…

8 more images…

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APA (6^th Edition):

Savala, P. (2016). Computing spectral data for Maass cusp forms using resonance. (Doctoral Dissertation). University of Iowa. Retrieved from https://ir.uiowa.edu/etd/3182

Chicago Manual of Style (16^th Edition):

Savala, Paul. “Computing spectral data for Maass cusp forms using resonance.” 2016. Doctoral Dissertation, University of Iowa. Accessed March 07, 2021. https://ir.uiowa.edu/etd/3182.

MLA Handbook (7^th Edition):

Savala, Paul. “Computing spectral data for Maass cusp forms using resonance.” 2016. Web. 07 Mar 2021.

Vancouver:

Savala P. Computing spectral data for Maass cusp forms using resonance. [Internet] [Doctoral dissertation]. University of Iowa; 2016. [cited 2021 Mar 07]. Available from: https://ir.uiowa.edu/etd/3182.

Council of Science Editors:

Savala P. Computing spectral data for Maass cusp forms using resonance. [Doctoral Dissertation]. University of Iowa; 2016. Available from: https://ir.uiowa.edu/etd/3182

University of Michigan

28. Klosin, Krzysztof. Congruences among automorphic forms on the unitary group U(2,2).

Degree: PhD, Pure Sciences, 2006, University of Michigan

URL: http://hdl.handle.net/2027.42/126079

► Let k be a positive integer divisible by 4, ℓ > k an odd prime, and f a normalized elliptic cuspidal eigenform of weight k… (more)

Subjects/Keywords: Automorphic Forms; Bloch-kato Conjecture; Congruences; Galois Representation; Galois Representations; L-functions; Selmer Group; Unitary Group U(2,2)

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APA (6^th Edition):

Klosin, K. (2006). Congruences among automorphic forms on the unitary group U(2,2). (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/126079

Chicago Manual of Style (16^th Edition):

Klosin, Krzysztof. “Congruences among automorphic forms on the unitary group U(2,2).” 2006. Doctoral Dissertation, University of Michigan. Accessed March 07, 2021. http://hdl.handle.net/2027.42/126079.

MLA Handbook (7^th Edition):

Klosin, Krzysztof. “Congruences among automorphic forms on the unitary group U(2,2).” 2006. Web. 07 Mar 2021.

Vancouver:

Klosin K. Congruences among automorphic forms on the unitary group U(2,2). [Internet] [Doctoral dissertation]. University of Michigan; 2006. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/2027.42/126079.

Council of Science Editors:

Klosin K. Congruences among automorphic forms on the unitary group U(2,2). [Doctoral Dissertation]. University of Michigan; 2006. Available from: http://hdl.handle.net/2027.42/126079

29. Conti, Andrea. Grande image de Galois pour familles p-adiques de formes automorphes de pente positive : Big Galois image for p-adic families of positive slope automorphic forms.

Degree: Docteur es, Mathématiques, 2016, Sorbonne Paris Cité

URL: http://www.theses.fr/2016USPCD081

►

Soit g = 1 ou 2 et p > 3 un nombre premier. Pour le groupe symplectique GSp2g, les systèmes de valeurs propres de Hecke… (more)

▼

Soit g = 1 ou 2 et p > 3 un nombre premier. Pour le groupe symplectique GSp2g, les systèmes de valeurs propres de Hecke apparaissant dans les espaces de formes automorphes classiques, d’un niveau modéré fixé et de poids variable, sont interpolés p-adiquement par un espace rigide analytique, la vari´et´e de Hecke pour GSp2g. Un sous-domaine suffisamment petit de cette variété peut être décrit comme l’espace rigide analytique associé `a une algèbre profinie T. Une composante irréductible de T est d´efinie par un anneau profini I et un morphisme θ : T → I. Dans le cas résiduellement irréductible on peut associer `a θ une représentation ρθ : Gal(Q/Q) → GSp2g(I). On étudie l’image de ρθ quand θ décrit une composante de pente positive de T. Pour g = 1 il s’agit d’un travail en commun avec A. Lovita et J. Tilouine. On suppose que g = 1 o`u que g = 2 et θ est résiduellement de type cube sym2trique. On montre que Im ρθ est “grande” et que sa taille est li´ee aux “congruences fortuites” de θ avec les transferts de familles pour groupes de rang plus petit. Plus précisement, on agrandit un sous-anneau I0de I[1/p] en un anneau B et on définit une sous-algèbre de Lie G de gsp2g(B) associée `a Im ρθ. On prouve qu’il existe un idéal non-nul l de I0 tel que l · sp2g(B) ⊂ G. Pour g = 1 les facteurs premiers de l correspondent aux points CM de la famille θ. Pour g = 2 les facteurs premiers de l correspondent `a des congruences fortuites de θ avec des sous-familles de dimension 0 ou 1, obtenues par des transferts de type cube sym´etrique de points ou familles de la courbe de Hecke pour GL2.

Let g = 1 or 2 and p > 3 be a prime. For the symplectic group GSp2g the Hecke eigensystems appearing in the spaces of classical automorphic forms, of a fixed tame level and varying weight, are p-adically interpolated by a rigid analytic space, the GSp2g-eigenvariety. A sufficiently small subdomain of the eigenvariety can be described as the rigid analytic space associated with a profinite algebra T. An irreducible component of T is defined by a profinite ring I and a morphism θ : T → I. In the residually irreducible case we can attach to θ a representation ρθ : Gal(Q/Q) → GSp2g(I). We study the image of ρθ when θ describes a positive slope component of T. In the case g = 1 this is a joint work with A. Iovita and J. Tilouine. Suppose either that g = 1 or that g = 2 and θ is residually of symmetric cube type. We prove that Im ρθ is “big” and that its size is related to the “accidental congruences” of θ with the subfamilies that are obtained as lifts of families for groups of smaller rank. More precisely, we enlarge a subring I0 of I[1/p] to a ring B and we define a Lie subalgebra G of gsp2g(B) associated with Im ρθ. We prove that there exists a non-zero ideal l of I0 such that l · sp2g(B) ⊂ G. For g = 1 the prime factors of l correspond to the CM points of the family θ. Such points do not define congruences between θ and a CM family, so we call them accidental congruence points. For g = 2 the prime factors of l correspond to accidental congruences…

Advisors/Committee Members: Tilouine, Jacques (thesis director).

Subjects/Keywords: Image de Galois; Familles p-adiques; Formes automorphes; Galois representations; Automorphic forms; P-Adic families

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APA (6^th Edition):

Conti, A. (2016). Grande image de Galois pour familles p-adiques de formes automorphes de pente positive : Big Galois image for p-adic families of positive slope automorphic forms. (Doctoral Dissertation). Sorbonne Paris Cité. Retrieved from http://www.theses.fr/2016USPCD081

Chicago Manual of Style (16^th Edition):

Conti, Andrea. “Grande image de Galois pour familles p-adiques de formes automorphes de pente positive : Big Galois image for p-adic families of positive slope automorphic forms.” 2016. Doctoral Dissertation, Sorbonne Paris Cité. Accessed March 07, 2021. http://www.theses.fr/2016USPCD081.

MLA Handbook (7^th Edition):

Conti, Andrea. “Grande image de Galois pour familles p-adiques de formes automorphes de pente positive : Big Galois image for p-adic families of positive slope automorphic forms.” 2016. Web. 07 Mar 2021.

Vancouver:

Conti A. Grande image de Galois pour familles p-adiques de formes automorphes de pente positive : Big Galois image for p-adic families of positive slope automorphic forms. [Internet] [Doctoral dissertation]. Sorbonne Paris Cité; 2016. [cited 2021 Mar 07]. Available from: http://www.theses.fr/2016USPCD081.

Council of Science Editors:

Conti A. Grande image de Galois pour familles p-adiques de formes automorphes de pente positive : Big Galois image for p-adic families of positive slope automorphic forms. [Doctoral Dissertation]. Sorbonne Paris Cité; 2016. Available from: http://www.theses.fr/2016USPCD081

ETH Zürich

30. Jana, Subhajit. Analytic Newvectors for GL(n,R) and Applications.

Degree: 2020, ETH Zürich

URL: http://hdl.handle.net/20.500.11850/418883

► We introduce an analytic archimedean analogue of some aspects of the classical non-archimedean newvector theory formulated by Casselman and Jacquet – Piatetski-Shapiro – Shalika. We relate the… (more)

Subjects/Keywords: Newvector; L-function; Automorphic forms; Whittaker functions; info:eu-repo/classification/ddc/510; Mathematics

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APA (6^th Edition):

Jana, S. (2020). Analytic Newvectors for GL(n,R) and Applications. (Doctoral Dissertation). ETH Zürich. Retrieved from http://hdl.handle.net/20.500.11850/418883

Chicago Manual of Style (16^th Edition):

Jana, Subhajit. “Analytic Newvectors for GL(n,R) and Applications.” 2020. Doctoral Dissertation, ETH Zürich. Accessed March 07, 2021. http://hdl.handle.net/20.500.11850/418883.

MLA Handbook (7^th Edition):

Jana, Subhajit. “Analytic Newvectors for GL(n,R) and Applications.” 2020. Web. 07 Mar 2021.

Vancouver:

Jana S. Analytic Newvectors for GL(n,R) and Applications. [Internet] [Doctoral dissertation]. ETH Zürich; 2020. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/20.500.11850/418883.

Council of Science Editors:

Jana S. Analytic Newvectors for GL(n,R) and Applications. [Doctoral Dissertation]. ETH Zürich; 2020. Available from: http://hdl.handle.net/20.500.11850/418883

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Open Access Theses and Dissertations