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Title:Topics in analytic number theory
Author(s):Pratt, Kyle
Director of Research:Ford, Kevin
Doctoral Committee Chair(s):Ahlgren, Scott
Doctoral Committee Member(s):Berndt, Bruce; Zaharescu, Alexandru
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):prime numbers
Dirichlet L-functions
Abstract: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 on work of Maynard and Friedlander-Iwaniec. Next, motivated by work of Iwaniec and Sarnak, we study the question of average nonvanishing of Dirichlet L-functions at the central point. Finally, in joint work with Siegfred Baluyot, we build on work of Soundararajan and synthesize our studies of primes and L-functions by examining Dirichlet L-functions of quadratic characters of prime conductor.
Issue Date:2019-04-12
Type:Text
URI:http://hdl.handle.net/2142/104815
Rights Information:Copyright 2019 Kyle Pratt
Date Available in IDEALS:2019-08-23
Date Deposited:2019-05


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