Topics in analytic number theory

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2019

Author dc:creator

• Pratt, Kyle

Contributors dc:contributor

• Ford, Kevin
• Ahlgren, Scott
• Berndt, Bruce
• Zaharescu, Alexandru

• prime numbers
• Dirichlet L-functions

Statement dc:rights

• Copyright 2019 Kyle Pratt

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/104815