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University of Illinois – Urbana-Champaign

1. Hutchinson, Suzanne C. Parabolas infiltrating the Ford circles.

Degree: MS, Mathematics, 2015, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/87952

► After briefly discussing classical results of Farey fractions and Ford circles, we define and study a new family of parabolas in connection with Ford circles…
(more)

Subjects/Keywords: none

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APA (6^{th} Edition):

Hutchinson, S. C. (2015). Parabolas infiltrating the Ford circles. (Thesis). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/87952

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):

Hutchinson, Suzanne C. “Parabolas infiltrating the Ford circles.” 2015. Thesis, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/87952.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Hutchinson, Suzanne C. “Parabolas infiltrating the Ford circles.” 2015. Web. 10 Jul 2020.

Vancouver:

Hutchinson SC. Parabolas infiltrating the Ford circles. [Internet] [Thesis]. University of Illinois – Urbana-Champaign; 2015. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/87952.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Hutchinson SC. Parabolas infiltrating the Ford circles. [Thesis]. University of Illinois – Urbana-Champaign; 2015. Available from: http://hdl.handle.net/2142/87952

Not specified: Masters Thesis or Doctoral Dissertation

University of Illinois – Urbana-Champaign

2. Xiao, Jiajie. Distribution of some arithmetic sequences.

Degree: PhD, 0439, 2013, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/45594

► In this thesis, we first study the correlations of some arithmetic sequences. We prove the existence of the limiting pair correlations of fractions with prime…
(more)

Subjects/Keywords: Number theory; analytic number theory.

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APA (6^{th} Edition):

Xiao, J. (2013). Distribution of some arithmetic sequences. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/45594

Chicago Manual of Style (16^{th} Edition):

Xiao, Jiajie. “Distribution of some arithmetic sequences.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/45594.

MLA Handbook (7^{th} Edition):

Xiao, Jiajie. “Distribution of some arithmetic sequences.” 2013. Web. 10 Jul 2020.

Vancouver:

Xiao J. Distribution of some arithmetic sequences. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/45594.

Council of Science Editors:

Xiao J. Distribution of some arithmetic sequences. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/45594

University of Illinois – Urbana-Champaign

3. Spiegelhalter, Paul. Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/50445

► K.T. Atanassov introduced the two arithmetic functions [ I(n) = \prod_{ν=1}^{k} p_ν^{1/α_ν} {and} R(n) = \prod_{ν=1}^{k} p_ν^{αv - 1} ] called the irrational factor and…
(more)

Subjects/Keywords: Number theory; Dirichlet series; Farey fractions

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APA (6^{th} Edition):

Spiegelhalter, P. (2014). Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/50445

Chicago Manual of Style (16^{th} Edition):

Spiegelhalter, Paul. “Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/50445.

MLA Handbook (7^{th} Edition):

Spiegelhalter, Paul. “Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations.” 2014. Web. 10 Jul 2020.

Vancouver:

Spiegelhalter P. Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/50445.

Council of Science Editors:

Spiegelhalter P. Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/50445

University of Illinois – Urbana-Champaign

4. Chaubey, Sneha. Correlations of sequences modulo one and statistics of geometrical objects associated to visible points.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/98203

► This thesis is divided into two major topics. In the first, we study the topic of distribution of sequences modulo one. In particular, we look…
(more)

Subjects/Keywords: Pair correlation; Riemann zeta; Visible lattice points

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APA (6^{th} Edition):

Chaubey, S. (2017). Correlations of sequences modulo one and statistics of geometrical objects associated to visible points. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/98203

Chicago Manual of Style (16^{th} Edition):

Chaubey, Sneha. “Correlations of sequences modulo one and statistics of geometrical objects associated to visible points.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/98203.

MLA Handbook (7^{th} Edition):

Chaubey, Sneha. “Correlations of sequences modulo one and statistics of geometrical objects associated to visible points.” 2017. Web. 10 Jul 2020.

Vancouver:

Chaubey S. Correlations of sequences modulo one and statistics of geometrical objects associated to visible points. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/98203.

Council of Science Editors:

Chaubey S. Correlations of sequences modulo one and statistics of geometrical objects associated to visible points. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/98203

University of Illinois – Urbana-Champaign

5. Malik, Amita. Partition asymptotics; zeros of zeta functions; and Apéry-like numbers.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/98291

► PART I G. H. Hardy and S. Ramanujan established an asymptotic formula for the number of unrestricted partitions of a positive integer, and claimed a…
(more)

Subjects/Keywords: Partitions; Arithmetic progressions; Parity; Asymptotics; Zeros; Riemann zeta function; Proportion; Apéry numbers

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APA (6^{th} Edition):

Malik, A. (2017). Partition asymptotics; zeros of zeta functions; and Apéry-like numbers. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/98291

Chicago Manual of Style (16^{th} Edition):

Malik, Amita. “Partition asymptotics; zeros of zeta functions; and Apéry-like numbers.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/98291.

MLA Handbook (7^{th} Edition):

Malik, Amita. “Partition asymptotics; zeros of zeta functions; and Apéry-like numbers.” 2017. Web. 10 Jul 2020.

Vancouver:

Malik A. Partition asymptotics; zeros of zeta functions; and Apéry-like numbers. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/98291.

Council of Science Editors:

Malik A. Partition asymptotics; zeros of zeta functions; and Apéry-like numbers. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/98291

University of Illinois – Urbana-Champaign

6. Kim, Eunmi. Root distribution of polynomials and distance sums on the unit circle.

Degree: PhD, 0439, 2013, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/44453

► Our first topic is the study of self-inversive polynomials. We establish sufficient conditions for self-inversive polynomials to have all zeros on the unit circle. We…
(more)

Subjects/Keywords: self-inversive polynomials; distance sum; unit circle

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APA (6^{th} Edition):

Kim, E. (2013). Root distribution of polynomials and distance sums on the unit circle. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/44453

Chicago Manual of Style (16^{th} Edition):

Kim, Eunmi. “Root distribution of polynomials and distance sums on the unit circle.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/44453.

MLA Handbook (7^{th} Edition):

Kim, Eunmi. “Root distribution of polynomials and distance sums on the unit circle.” 2013. Web. 10 Jul 2020.

Vancouver:

Kim E. Root distribution of polynomials and distance sums on the unit circle. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/44453.

Council of Science Editors:

Kim E. Root distribution of polynomials and distance sums on the unit circle. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/44453

University of Illinois – Urbana-Champaign

7. Konstantoulas, Ioannis. Effective multiple mixing in Weyl chamber actions.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/49459

► In this work, we prove effective decay of certain multiple correlation coefficients for Weyl chamber actions of semidirect products of semisimple groups with G-vector spaces.…
(more)

Subjects/Keywords: semisimple groups; semidirect products; effective multiple mixing; Weyl chamber actions

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APA (6^{th} Edition):

Konstantoulas, I. (2014). Effective multiple mixing in Weyl chamber actions. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/49459

Chicago Manual of Style (16^{th} Edition):

Konstantoulas, Ioannis. “Effective multiple mixing in Weyl chamber actions.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/49459.

MLA Handbook (7^{th} Edition):

Konstantoulas, Ioannis. “Effective multiple mixing in Weyl chamber actions.” 2014. Web. 10 Jul 2020.

Vancouver:

Konstantoulas I. Effective multiple mixing in Weyl chamber actions. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/49459.

Council of Science Editors:

Konstantoulas I. Effective multiple mixing in Weyl chamber actions. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/49459

University of Illinois – Urbana-Champaign

8. Schultz, Daniel. Cubic theta functions and identities for Appell's F1 function.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/50667

► This thesis is centered around three topics: the theory of the cubic theta functions as functions of two analytic variables, cubic modular equations, and a…
(more)

Subjects/Keywords: cubic theta functions; modular equations; appell hypergeometric; picard modular forms

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APA (6^{th} Edition):

Schultz, D. (2014). Cubic theta functions and identities for Appell's F1 function. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/50667

Chicago Manual of Style (16^{th} Edition):

Schultz, Daniel. “Cubic theta functions and identities for Appell's F1 function.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/50667.

MLA Handbook (7^{th} Edition):

Schultz, Daniel. “Cubic theta functions and identities for Appell's F1 function.” 2014. Web. 10 Jul 2020.

Vancouver:

Schultz D. Cubic theta functions and identities for Appell's F1 function. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/50667.

Council of Science Editors:

Schultz D. Cubic theta functions and identities for Appell's F1 function. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/50667

University of Illinois – Urbana-Champaign

9. Phaovibul, Mtip Easter. Extensions of Selberg-Delange method.

Degree: PhD, Mathematics, 2015, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/78348

► This dissertation involves two topics in analytic number theory. The first topic focuses on extensions of the Selberg-Delange Method, which are discussed in Chapters 2…
(more)

Subjects/Keywords: Multiple Zeta function; Selberg-Delange Method; Asymptotic; Riemann Zeta function

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APA (6^{th} Edition):

Phaovibul, M. E. (2015). Extensions of Selberg-Delange method. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/78348

Chicago Manual of Style (16^{th} Edition):

Phaovibul, Mtip Easter. “Extensions of Selberg-Delange method.” 2015. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/78348.

MLA Handbook (7^{th} Edition):

Phaovibul, Mtip Easter. “Extensions of Selberg-Delange method.” 2015. Web. 10 Jul 2020.

Vancouver:

Phaovibul ME. Extensions of Selberg-Delange method. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2015. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/78348.

Council of Science Editors:

Phaovibul ME. Extensions of Selberg-Delange method. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2015. Available from: http://hdl.handle.net/2142/78348

University of Illinois – Urbana-Champaign

10. Yuttanan, Boonrod. Modular equations and Ramanujan's cubic and quartic theories of theta functions.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/29552

► In this thesis, we prove several identities involving Ramanujan's general theta function. In Chapter 2, we give proofs for new Ramanujan type modular equations discovered…
(more)

Subjects/Keywords: modular equations; theta-functions; cubic theta-functions; eta-functions; partitions; colored partitions; continued fraction; power series expansion; periodicity of sign of coefficients; infinite series

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APA (6^{th} Edition):

Yuttanan, B. (2012). Modular equations and Ramanujan's cubic and quartic theories of theta functions. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/29552

Chicago Manual of Style (16^{th} Edition):

Yuttanan, Boonrod. “Modular equations and Ramanujan's cubic and quartic theories of theta functions.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/29552.

MLA Handbook (7^{th} Edition):

Yuttanan, Boonrod. “Modular equations and Ramanujan's cubic and quartic theories of theta functions.” 2012. Web. 10 Jul 2020.

Vancouver:

Yuttanan B. Modular equations and Ramanujan's cubic and quartic theories of theta functions. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/29552.

Council of Science Editors:

Yuttanan B. Modular equations and Ramanujan's cubic and quartic theories of theta functions. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/29552

11. Pratt, Kyle. Topics in analytic number theory.

Degree: PhD, Mathematics, 2019, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/104815

► We investigate properties of prime numbers and L-functions, and interactions between these two topics. First, we discuss the problem of primes in thin sequences, expanding…
(more)

Subjects/Keywords: prime numbers; Dirichlet L-functions

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APA (6^{th} Edition):

Pratt, K. (2019). Topics in analytic number theory. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/104815

Chicago Manual of Style (16^{th} Edition):

Pratt, Kyle. “Topics in analytic number theory.” 2019. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/104815.

MLA Handbook (7^{th} Edition):

Pratt, Kyle. “Topics in analytic number theory.” 2019. Web. 10 Jul 2020.

Vancouver:

Pratt K. Topics in analytic number theory. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2019. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/104815.

Council of Science Editors:

Pratt K. Topics in analytic number theory. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2019. Available from: http://hdl.handle.net/2142/104815

12. Tamazyan, Albert. Visibility of lattice points in high dimensional spaces and extreme values of combinations of Dirichlet L-functions.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101560

► This thesis is divided into three major topics. In the first, we study questions concerning the distribution of lattice points in dimensions two and higher.…
(more)

Subjects/Keywords: Visible Points; Farey Sequences

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APA (6^{th} Edition):

Tamazyan, A. (2018). Visibility of lattice points in high dimensional spaces and extreme values of combinations of Dirichlet L-functions. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101560

Chicago Manual of Style (16^{th} Edition):

Tamazyan, Albert. “Visibility of lattice points in high dimensional spaces and extreme values of combinations of Dirichlet L-functions.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/101560.

MLA Handbook (7^{th} Edition):

Tamazyan, Albert. “Visibility of lattice points in high dimensional spaces and extreme values of combinations of Dirichlet L-functions.” 2018. Web. 10 Jul 2020.

Vancouver:

Tamazyan A. Visibility of lattice points in high dimensional spaces and extreme values of combinations of Dirichlet L-functions. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/101560.

Council of Science Editors:

Tamazyan A. Visibility of lattice points in high dimensional spaces and extreme values of combinations of Dirichlet L-functions. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101560

13. Roy, Arindam. Ramanujan's identities, Voronoi summation formula, and zeros of partial sums of zeta and L-functions.

Degree: PhD, Mathematics, 2015, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/88129

► The focus of the first part of the thesis commences with an examination of two pages in Ramanujan's lost notebook, pages 336 and 335. A…
(more)

Subjects/Keywords: Ramanujan; Voronoi summation formula; Divisor problem; Dedekind zeta function; Dirichlet polynomial; Distribution of zeros; Hecke L-functions; Approximate functional equation; Proportion of zeros on the critical line

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APA (6^{th} Edition):

Roy, A. (2015). Ramanujan's identities, Voronoi summation formula, and zeros of partial sums of zeta and L-functions. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/88129

Chicago Manual of Style (16^{th} Edition):

Roy, Arindam. “Ramanujan's identities, Voronoi summation formula, and zeros of partial sums of zeta and L-functions.” 2015. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/88129.

MLA Handbook (7^{th} Edition):

Roy, Arindam. “Ramanujan's identities, Voronoi summation formula, and zeros of partial sums of zeta and L-functions.” 2015. Web. 10 Jul 2020.

Vancouver:

Roy A. Ramanujan's identities, Voronoi summation formula, and zeros of partial sums of zeta and L-functions. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2015. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/88129.

Council of Science Editors:

Roy A. Ramanujan's identities, Voronoi summation formula, and zeros of partial sums of zeta and L-functions. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2015. Available from: http://hdl.handle.net/2142/88129

14. Heersink, Byron Nicholas. Applications of dynamical systems to Farey sequences and continued fractions.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/97300

► This thesis explores three main topics in the application of ergodic theory and dynamical systems to equidistribution and spacing statistics in number theory. The first…
(more)

Subjects/Keywords: Equidistribution; Gap distribution; Farey fractions; Horocycle flow; Geodesic flow; Farey map; Continued fractions; Transfer operator

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APA (6^{th} Edition):

Heersink, B. N. (2017). Applications of dynamical systems to Farey sequences and continued fractions. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/97300

Chicago Manual of Style (16^{th} Edition):

Heersink, Byron Nicholas. “Applications of dynamical systems to Farey sequences and continued fractions.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/97300.

MLA Handbook (7^{th} Edition):

Heersink, Byron Nicholas. “Applications of dynamical systems to Farey sequences and continued fractions.” 2017. Web. 10 Jul 2020.

Vancouver:

Heersink BN. Applications of dynamical systems to Farey sequences and continued fractions. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/97300.

Council of Science Editors:

Heersink BN. Applications of dynamical systems to Farey sequences and continued fractions. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/97300

15. Merriman, Claire. Geometric and ergodic properties of certain classes of continued fractions.

Degree: PhD, Mathematics, 2019, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/105632

► Continued fractions are systematically studied in number theory, dynamical systems, and ergodic theory, and appear frequently in other areas of mathematics. The first part of…
(more)

Subjects/Keywords: ergodic theory; continued fractions; cutting sequence

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APA (6^{th} Edition):

Merriman, C. (2019). Geometric and ergodic properties of certain classes of continued fractions. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/105632

Chicago Manual of Style (16^{th} Edition):

Merriman, Claire. “Geometric and ergodic properties of certain classes of continued fractions.” 2019. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/105632.

MLA Handbook (7^{th} Edition):

Merriman, Claire. “Geometric and ergodic properties of certain classes of continued fractions.” 2019. Web. 10 Jul 2020.

Vancouver:

Merriman C. Geometric and ergodic properties of certain classes of continued fractions. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2019. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/105632.

Council of Science Editors:

Merriman C. Geometric and ergodic properties of certain classes of continued fractions. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2019. Available from: http://hdl.handle.net/2142/105632

16. Xu, Ping. Identities involving theta functions and analogues of theta functions.

Degree: PhD, 0439, 2013, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/45365

► My dissertation is mainly about various identities involving theta functions and analogues of theta functions. In Chapter 1, we give a completely elementary proof of…
(more)

Subjects/Keywords: Circular summation formula; elementary proof; two-dimensional lattice sums; Poisson equation; theta functions; analogue of theta functions; analogue of Gauss sums

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

APA (6^{th} Edition):

Xu, P. (2013). Identities involving theta functions and analogues of theta functions. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/45365

Chicago Manual of Style (16^{th} Edition):

Xu, Ping. “Identities involving theta functions and analogues of theta functions.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/45365.

MLA Handbook (7^{th} Edition):

Xu, Ping. “Identities involving theta functions and analogues of theta functions.” 2013. Web. 10 Jul 2020.

Vancouver:

Xu P. Identities involving theta functions and analogues of theta functions. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/45365.

Council of Science Editors:

Xu P. Identities involving theta functions and analogues of theta functions. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/45365

17. Vandehey, Joseph. Error term improvements for van der Corput transforms.

Degree: PhD, 0439, 2013, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/44398

► We improve the error term in the van der Corput transform for exponential sums, ∑ g(n) exp(2 π i f(n)). For many smooth functions g…
(more)

Subjects/Keywords: Asymptotic analysis; exponential sum; trigonometric sum; van der Corput transform

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

APA (6^{th} Edition):

Vandehey, J. (2013). Error term improvements for van der Corput transforms. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/44398

Chicago Manual of Style (16^{th} Edition):

Vandehey, Joseph. “Error term improvements for van der Corput transforms.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/44398.

MLA Handbook (7^{th} Edition):

Vandehey, Joseph. “Error term improvements for van der Corput transforms.” 2013. Web. 10 Jul 2020.

Vancouver:

Vandehey J. Error term improvements for van der Corput transforms. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/44398.

Council of Science Editors:

Vandehey J. Error term improvements for van der Corput transforms. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/44398

18. Lansing, Jennifer. On the Stern sequence and a related sequence.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/49483

► In this dissertation, we discuss properties of the Stern sequence, denoted by s(n), and define a related sequence. First, we give a brief historical background…
(more)

Subjects/Keywords: Stern sequence

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

APA (6^{th} Edition):

Lansing, J. (2014). On the Stern sequence and a related sequence. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/49483

Chicago Manual of Style (16^{th} Edition):

Lansing, Jennifer. “On the Stern sequence and a related sequence.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/49483.

MLA Handbook (7^{th} Edition):

Lansing, Jennifer. “On the Stern sequence and a related sequence.” 2014. Web. 10 Jul 2020.

Vancouver:

Lansing J. On the Stern sequence and a related sequence. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/49483.

Council of Science Editors:

Lansing J. On the Stern sequence and a related sequence. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/49483

19. Polanco Encarnacion, Geremias. Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/34298

► This dissertation is divided into three main sections. The main result of Section 1 is that, for a,b>1, irrational, the quantity log (a/b) is ``not…
(more)

Subjects/Keywords: Beatty Sequence; Sturmian Sequence; characteristic Sequence; Frullani's integral; Steinhaus Theorem; Three Gap Theorem; Kloosterman Sums; Farey Fractions

Record Details Similar Records

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

APA (6^{th} Edition):

Polanco Encarnacion, G. (2012). Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/34298

Chicago Manual of Style (16^{th} Edition):

Polanco Encarnacion, Geremias. “Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/34298.

MLA Handbook (7^{th} Edition):

Polanco Encarnacion, Geremias. “Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory.” 2012. Web. 10 Jul 2020.

Vancouver:

Polanco Encarnacion G. Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/34298.

Council of Science Editors:

Polanco Encarnacion G. Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/34298

20. Tran, Khang. Discriminants: calculation, properties, and connection to the root distribution of polynomials with rational generating functions.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/34354

► This research centers on discriminants and how discriminants and their q-analogues relate to the root distribution of polynomials. This topic includes the connections between the…
(more)

Subjects/Keywords: discriminant; resultant; root distribution

Record Details Similar Records

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

APA (6^{th} Edition):

Tran, K. (2012). Discriminants: calculation, properties, and connection to the root distribution of polynomials with rational generating functions. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/34354

Chicago Manual of Style (16^{th} Edition):

Tran, Khang. “Discriminants: calculation, properties, and connection to the root distribution of polynomials with rational generating functions.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/34354.

MLA Handbook (7^{th} Edition):

Tran, Khang. “Discriminants: calculation, properties, and connection to the root distribution of polynomials with rational generating functions.” 2012. Web. 10 Jul 2020.

Vancouver:

Tran K. Discriminants: calculation, properties, and connection to the root distribution of polynomials with rational generating functions. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/34354.

Council of Science Editors:

Tran K. Discriminants: calculation, properties, and connection to the root distribution of polynomials with rational generating functions. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/34354

21. Mak, Kit Ho. On congruence function fields with many rational places.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/34193

► In this thesis, we study congruence function fields, in particular those with many rational places. This thesis consists of three parts, the first two parts…
(more)

Subjects/Keywords: function fields; maximal curves; Ihara constants; asymptotic bounds; subcover problem

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

APA (6^{th} Edition):

Mak, K. H. (2012). On congruence function fields with many rational places. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/34193

Chicago Manual of Style (16^{th} Edition):

Mak, Kit Ho. “On congruence function fields with many rational places.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/34193.

MLA Handbook (7^{th} Edition):

Mak, Kit Ho. “On congruence function fields with many rational places.” 2012. Web. 10 Jul 2020.

Vancouver:

Mak KH. On congruence function fields with many rational places. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/34193.

Council of Science Editors:

Mak KH. On congruence function fields with many rational places. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/34193

University of Illinois – Urbana-Champaign

22. Kim, Byung Chan. Arithmetic of partition functions and q-combinatorics.

Degree: PhD, 0439, 2010, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/15588

► Integer partitions play important roles in diverse areas of mathematics such as q-series, the theory of modular forms, representation theory, symmetric functions and mathematical physics.…
(more)

Subjects/Keywords: Partitions; Partition congruences; q-series; Modular forms; Combinatorial proof; Mock theta functions

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

APA (6^{th} Edition):

Kim, B. C. (2010). Arithmetic of partition functions and q-combinatorics. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/15588

Chicago Manual of Style (16^{th} Edition):

Kim, Byung Chan. “Arithmetic of partition functions and q-combinatorics.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/15588.

MLA Handbook (7^{th} Edition):

Kim, Byung Chan. “Arithmetic of partition functions and q-combinatorics.” 2010. Web. 10 Jul 2020.

Vancouver:

Kim BC. Arithmetic of partition functions and q-combinatorics. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/15588.

Council of Science Editors:

Kim BC. Arithmetic of partition functions and q-combinatorics. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/15588

University of Illinois – Urbana-Champaign

23. Dewar, Michael P. Congruences in modular, Jacobi, Siegel, and mock modular forms with applications.

Degree: PhD, 0439, 2010, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/16054

► We study congruences in the coefficients of modular and other automorphic forms. Ramanujan famously found congruences for the partition function like p(5n+4) = 0 mod…
(more)

Subjects/Keywords: Ramanujan congruences; Tate cycle; heat cycle; Fourier coefficients; Modular forms; reduced modular forms; Jacobi forms; Siegel modular forms

Record Details Similar Records

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

APA (6^{th} Edition):

Dewar, M. P. (2010). Congruences in modular, Jacobi, Siegel, and mock modular forms with applications. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/16054

Chicago Manual of Style (16^{th} Edition):

Dewar, Michael P. “Congruences in modular, Jacobi, Siegel, and mock modular forms with applications.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/16054.

MLA Handbook (7^{th} Edition):

Dewar, Michael P. “Congruences in modular, Jacobi, Siegel, and mock modular forms with applications.” 2010. Web. 10 Jul 2020.

Vancouver:

Dewar MP. Congruences in modular, Jacobi, Siegel, and mock modular forms with applications. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/16054.

Council of Science Editors:

Dewar MP. Congruences in modular, Jacobi, Siegel, and mock modular forms with applications. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/16054

University of Illinois – Urbana-Champaign

24. Dennison, Melissa A. A sequence related to the Stern sequence.

Degree: PhD, 0439, 2010, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/16821

► In this dissertation we de???ne and study a two-parameter family of recursive sequences which we call the bow sequences. The general bow sequence is de???ned…
(more)

Subjects/Keywords: Stern sequence; recursive sequence; generating function; Fibonacci

Record Details Similar Records

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

APA (6^{th} Edition):

Dennison, M. A. (2010). A sequence related to the Stern sequence. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/16821

Chicago Manual of Style (16^{th} Edition):

Dennison, Melissa A. “A sequence related to the Stern sequence.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 10, 2020. http://hdl.handle.net/2142/16821.

MLA Handbook (7^{th} Edition):

Dennison, Melissa A. “A sequence related to the Stern sequence.” 2010. Web. 10 Jul 2020.

Vancouver:

Dennison MA. A sequence related to the Stern sequence. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2142/16821.

Council of Science Editors:

Dennison MA. A sequence related to the Stern sequence. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/16821