Director of Research (if dissertation) or Advisor (if thesis)
Ford, Kevin
Doctoral Committee Chair(s)
Ahlgren, Scott
Committee Member(s)
Berndt, Bruce
Zaharescu, Alexandru
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
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