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

TL;DR

This paper investigates wide moments of Dirichlet L-functions using Lerch zeta function properties, deriving asymptotic formulas and applications to non-vanishing, extending previous results by Heath-Brown.

Contribution

It provides an asymptotic expansion for wide moments of Dirichlet L-functions with arbitrary twists, advancing the understanding of their analytic behavior.

Findings

Derived asymptotic formulas for wide moments

Extended Heath-Brown's results to broader settings

Applied results to non-vanishing of 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.