Topics in analytic number theory

prime numbers;Dirichlet L-functions

Pratt, Kyle

关键词: prime numbers;    Dirichlet L-functions;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/104815/PRATT-DISSERTATION-2019.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.