Kaisa Matomäki: 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.