A standard zero free region for Rankin-Selberg L-functions

TL;DR

This paper establishes a zero-free region for Rankin-Selberg L-functions associated with Maass forms on GL(n), extending previous results by using Eisenstein series theory.

Contribution

It introduces a new method based on Eisenstein series to derive zero-free regions for Rankin-Selberg L-functions without requiring self-duality.

Findings

Zero-free region for $L(s, f\times \widetilde{f})$ established

Method generalizes Sarnak's approach using Eisenstein series

Applicable to non-self dual Maass forms on GL(n)

Abstract

A standard zero free region is obtained for Rankin Selberg L-functions $L(s, f\times \widetilde{f})$ where $f$ is an almost everywhere tempered Maass form on $GL(n)$ and $f$ is not necessarily self dual. The method is based on the theory of Eisenstein series generalizing a work of Sarnak.