Partition into primes

It is an important topic in analytic number theory to understand the moments of the Riemann zeta-function and other L-functions. In this project the student will study the connections involving moments of L-functions in families with random matrix theory. Specifically, the main subject of study will be the Euler-Hadamard hybrid formula. Other topics include the study of distribution of zeros of L-functions such as one-level density and pair correlation. For the final parts of the project the student will focus on function field analogues of the Hybrid formula for different families of L-functions over function fields of higher genus.