Moments of Dirichlet $L$-functions

Abstract: I will discuss my on-going joint work with Vorrapan Chandee, Xiannan Li, and Maksym Radziwill on moments of Dirichlet $L$-functions. I will mostly concentrate on our result giving an asymptotic formula for the eighth moment of Dirichlet L-functions averaged over primitive characters modulo $q$, over all moduli $q \leq Q$ and with a short average on the critical line. Previously this result was known only conditionally on the Generalized Riemann Hypothesis by work of Chandee and Li whereas a corresponding unconditional result for the sixth moment was known by work of Conrey, Iwaniec and Soundararajan..

number theory

Audience: researchers in the topic

IML Number Theory semester (spring 2021)