Moments of characteristic polynomials of random matrices and L-functions over function fields

The project will investigate several problems about mean values of arithmetic functions in the context of function fields. Specifically, it will focus on the mean value of arithmetic functions in short intervals and in arithmetic progressions using the new techniques developed by Keating and Rudnick. Another aspect of the project is the study of mean values of L-functions over function fields focusing on the study of the distribution of zeros and their statistics.