Wide moments of $L$-functions II: Dirichlet $L$-functions

Abstract

We study wide moments of Dirichlet $L$-functions using analytic properties of the Lerch zeta function. Among other things we obtain an asymptotic expansion of wide moments of Dirichlet $L$-functions (with arbitrary twists) extending results of Heath-Brown. We also give applications to non-vanishing.

arXiv commentProposition 2.4 in the previous version was wrong (note that this does not affect any of the results stated in the introduction). We have corrected the statement and proof, 20 pages