On moments of L-functions over Dirichlet characters

TL;DR

This paper provides a new proof for the asymptotic expansion of the second moment of Dirichlet L-functions and extends similar results to twisted first moments of Hecke-Maass L-functions, advancing understanding of L-function moments.

Contribution

It introduces a novel proof technique for Heath-Brown's asymptotic expansion and applies it to derive new results for Hecke-Maass L-functions.

Findings

Confirmed the full asymptotic expansion for the second moment of Dirichlet L-functions.

Derived a new asymptotic expansion for a twisted first moment of Hecke-Maass L-functions.

Abstract

We give a new proof of Heath-Brown's full asymptotic expansion for the second moment of Dirichlet L-functions and we obtain a corresponding asymptotic expansion for a twisted first moment of Hecke-Maass L-functions.