Dirichlet series constructed from periods of automorphic forms

TL;DR

This paper investigates Dirichlet series derived from automorphic form periods, demonstrating their analytic continuation across the entire complex plane, which advances understanding of their complex analysis properties.

Contribution

It introduces a new class of Dirichlet series from automorphic form periods and proves their analytic continuation, extending previous results in automorphic forms and number theory.

Findings

Dirichlet series have analytic continuation to the whole complex plane

Established properties of these series related to automorphic forms

Enhanced understanding of the analytic structure of automorphic periods

Abstract

We consider certain Dirichlet series of Selberg type, constructed from periods of automorphic forms. We study analytic properties of these Dirichlet series and show that they have analytic continuation to the whole complex plane.