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

2025/08/17 by Agniva Dasgupta, Rizwanur Khan, Dasgupta, Agniva +3
Computer Science · Mathematics · #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2508.12401

openalex publication_date 2025/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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