Browsing by Author "Papanikolas, Matthew"
Now showing items 1-15 of 15
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Khaochim, Narissara (2021-04-15)In this dissertation, we give two main results. First, we use the Bruinier-Ono formula to give an asymptotic formula for the partition function $p(n)$ with an effective bound on the error term. Second, we give an asymptotic ...
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Barquero Sanchez, Adrian Alberto (2016-08-05)In this thesis we start by giving a quick review of the classical Chowla-Selberg formula. We then recall a conjecture of Colmez which relates the Faltings height of an abelian variety with complex multiplication by the ...
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Frechette, Sharon; Ono, Ken; Papanikolas, Matthew (Proceedings of the National Academy of Sciences of the United States of America, 2004)
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Creamer, Daniel Edward (2018-08-07)The dissertation introduces a computational approach to classifying low rank modular categories up to their modular data. The modular data of a modular category is a pair of matrices, (S; T). Virtually all the numerical ...
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Huang, Wei Cheng (2023-06-01)We present special value results of convolutions of Goss and Pellarin L-series attached to Drinfeld modules that take values in Tate algebras by Papanikolas and the author. Following the same framework, we establish special ...
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Rivera Montes De Oca, Jose Manuel (2017-07-27)We start with some Fourier analysis on cyclic groups as the base case. This theory comes along with some basic notions about character theory. So, we develop some properties of the additive characters of Z/qZ. Formulas ...
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Fuselier, Jenny G. (2009-05-15)The theory of hypergeometric functions over finite fields was developed in the mid- 1980s by Greene. Since that time, connections between these functions and elliptic curves and modular forms have been investigated by ...
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Vega Veglio, Maria V. (2010-07-14)Classical hypergeometric functions and their relations to counting points on curves over finite fields have been investigated by mathematicians since the beginnings of 1900. In the mid 1980s, John Greene developed the ...
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Samart, Detchat (2014-08-04)The logarithmic Mahler measure of a nonzero n-variable Laurent polynomial P ∈ C [X_1^(±1),…,X_n^(±1) ], denoted by m(P), is defined to be the arithmetic mean of log|P| over the n-dimensional torus. It has been proved or ...
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Khaochim, Chalinee (2021-04-12)The purpose of this research is to study Drinfeld modules, tensor product of Drinfeld modules, their rigid analytic trivializations, and their periods. A formula for rigid analytic trivializations for Drinfeld modules was ...
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Lutes, Brad Aubrey (2010-10-12)Let K be the function field of an irreducible, smooth projective curve X defined over Fq. Let [lemniscate] be a fixed point on X and let A [a subset of or is equal to] K be the Dedekind domain of functions which are regular ...
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Ganguly, Soumendra (2023-08-02)Let φ be the symmetric-square lift of an SL2(Z) Hecke-Maass form. Let q be an odd cube-free positive integer, and let χ be a primitive Dirichlet character modulo q such that χ is not quadratic. Let f be an even Hecke-normalized ...
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Green, Nathan Eric (2018-05-23)We study tensor powers of rank 1 sign-normalized Drinfeld A-modules, where A is the coordinate ring of an elliptic curve over a finite field. Using the theory of A-motives, we find explicit formulas for the A-action of ...
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Garcia, Bradford Alexander (2022-07-28)We compute the second moment of Dirichlet L-functions along a coset at the central point, achieving an asymptotic result in the q-aspect.
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Zeng, Guchao (2017-06-23)The first part of the dissertation is mainly from my first paper joint with my advisor Papanikolas and the second part will be our second paper. In 1973, Serre introduced p-adic modular forms for a fixed prime p, which ...