Reciprocity for GL(2) L-functions twisted by Dirichlet characters

TL;DR

This paper establishes a new reciprocity relation for the first moment of GL(2) L-functions twisted by Dirichlet characters, extending previous results with a simplified approach.

Contribution

It introduces a novel reciprocity formula for GL(2) L-functions twisted by Dirichlet characters, broadening the scope of existing reciprocity relations.

Findings

Derived a reciprocity relation connecting moments of GL(2) L-functions

Extended previous results with a simpler proof technique

Enhanced understanding of the symmetry in twisted L-functions

Abstract

A formula connecting a moment of L-functions and a dual moment in a way that interchanges the roles of certain key parameters on both sides is known as a reciprocity relation. We establish a reciprocity relation for a first moment of GL(2) L-functions twisted by Dirichlet characters. This extends, via a new and simple argument, some results of Bettin, Drappeau, and Nordentoft.