Maksym Radziwill, University of Texas at Austin
I will discuss recent work with Fai Chandee, Xiannan Li
and Kaisa Matomaki in which we obtain a power-saving asymptotic for the
sixth moment of Dirichlet L-functions in the large family averaging
over primitive characters modulo q and moduli q. Previously this was
known with an additional short averaging in the t-aspect, following work
of Conrey, Iwaniec and Soundararajan on the asymptotic large sieve.
Removing the t-average leads to unbalanced sums in the moment problem
and requires input from spectral theory. This is in contrast with earlier work
of Conrey, Iwaniec and Soundararajan which relied exclusively on divisor
switching thanks to the presence of the t-average.