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You searched for subject:(paramodular forms). Showing records 1 – 2 of 2 total matches.

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University of Oklahoma

1. Roy, Manami. ELLIPTIC CURVES AND PARAMODULAR FORMS.

Degree: PhD, 2019, University of Oklahoma

There is a lifting from a non-CM elliptic curve E/ℚ to a cuspidal paramodular newform f of degree 2 and weight 3 given by the symmetric cube map. We find a description of the level of f in terms of the coefficients of the Weierstrass equation of E. In order to compute the paramodular level, we need a detailed description of the local representations πp of \GL(2,ℚp) attached to E/ℚp, where π\cong\bigotimes\limitspπp is the cuspidal automorphic representation of \GL(2,\mathbb{A}) associated with E/ℚ. We use the available description of the local representations of \GL(2,ℚp) attached to E for p  ≥  5 and determine the local representation of \GL(2,ℚ3) attached to E. In fact, we study the representations of \GL(2, K) attached to E/K for any non-archimedean local field K of characteristic 0 and residue characteristic 3. Advisors/Committee Members: Schmidt, Ralf (advisor), Dunn, Anne (committee member), Lifschitz, Lucy (committee member), Pitale, Ameya (committee member), Roche, Alan (committee member).

Subjects/Keywords: elliptic curves; paramodular forms; symmetric cube lifting

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

APA (6th Edition):

Roy, M. (2019). ELLIPTIC CURVES AND PARAMODULAR FORMS. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/321046

Chicago Manual of Style (16th Edition):

Roy, Manami. “ELLIPTIC CURVES AND PARAMODULAR FORMS.” 2019. Doctoral Dissertation, University of Oklahoma. Accessed January 23, 2021. http://hdl.handle.net/11244/321046.

MLA Handbook (7th Edition):

Roy, Manami. “ELLIPTIC CURVES AND PARAMODULAR FORMS.” 2019. Web. 23 Jan 2021.

Vancouver:

Roy M. ELLIPTIC CURVES AND PARAMODULAR FORMS. [Internet] [Doctoral dissertation]. University of Oklahoma; 2019. [cited 2021 Jan 23]. Available from: http://hdl.handle.net/11244/321046.

Council of Science Editors:

Roy M. ELLIPTIC CURVES AND PARAMODULAR FORMS. [Doctoral Dissertation]. University of Oklahoma; 2019. Available from: http://hdl.handle.net/11244/321046


University of Oklahoma

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

Degree: PhD, 2018, University of Oklahoma

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 Siegel congruence subgroups. Moreover, we give a computational algorithm for describing the one-dimensional cusps of the Satake compactifications for the Siegel congruence subgroups in the case of degree two for arbitrary levels. As an application of the results thus obtained, we calculate the co-dimensions of the spaces of cusp forms in the spaces of modular forms of degree two with respect to Siegel congruence subgroups of levels not divisible by 8. Advisors/Committee Members: Schmidt, Ralf (advisor), Cruz, J.R. (committee member), Pitale, Ameya (committee member), Przebinda, Tomasz (committee member), Roche, Alan (committee member).

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

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

APA (6th 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 (16th Edition):

Shukla, Alok. “On Klingen Eisenstein series with levels.” 2018. Doctoral Dissertation, University of Oklahoma. Accessed January 23, 2021. http://hdl.handle.net/11244/299326.

MLA Handbook (7th Edition):

Shukla, Alok. “On Klingen Eisenstein series with levels.” 2018. Web. 23 Jan 2021.

Vancouver:

Shukla A. On Klingen Eisenstein series with levels. [Internet] [Doctoral dissertation]. University of Oklahoma; 2018. [cited 2021 Jan 23]. 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

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