Browsing by Author "Papanikolas, Matthew"
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Combinatorics of traces of Hecke operators
Frechette, Sharon; Ono, Ken; Papanikolas, Matthew (Proceedings of the National Academy of Sciences of the United States of America, 2004) 
A Computational Approach to Classifying Low Rank Modular Tensor Categories
Creamer, Daniel Edward (20180807)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 ... 
Fourier Analysis on Finite Groups
Rivera Montes De Oca, Jose Manuel (20170727)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 ... 
Hypergeometric functions over finite fields and relations to modular forms and elliptic curves
Fuselier, Jenny G. (20090515)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 ... 
Hypergeometric functions over finite fields and their relations to algebraic curves.
Vega Veglio, Maria V. (20100714)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 ... 
Mahler Measures of Hypergeometric Families of CalabiYau Varieties
Samart, Detchat (20140804)The logarithmic Mahler measure of a nonzero nvariable Laurent polynomial P ∈ C [X_1^(±1),…,X_n^(±1) ], denoted by m(P), is defined to be the arithmetic mean of logP over the ndimensional torus. It has been proved or ... 
Special Values of the Goss Lfunction and Special Polynomials
Lutes, Brad Aubrey (20101012)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 ... 
Tensor Powers of Drinfeld Modules and Zeta Values
Green, Nathan Eric (20180523)We study tensor powers of rank 1 signnormalized Drinfeld Amodules, where A is the coordinate ring of an elliptic curve over a finite field. Using the theory of Amotives, we find explicit formulas for the Aaction of ... 
The ChowlaSelberg Formula for CM Fields and the Colmez Conjecture
Barquero Sanchez, Adrian Alberto (20160805)In this thesis we start by giving a quick review of the classical ChowlaSelberg formula. We then recall a conjecture of Colmez which relates the Faltings height of an abelian variety with complex multiplication by the ... 
Theta Operators on vadic Modular Forms and vadic Families of Goss Polynomials and Eisenstein Series
Zeng, Guchao (20170623)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 padic modular forms for a fixed prime p, which ...