# Standard Zero-Free Regions for Rankin--Selberg L-Functions via Sieve Theory

## TL;DR

This paper provides a straightforward proof establishing a standard zero-free region in the t-aspect for Rankin--Selberg L-functions associated with automorphic representations, enhancing understanding of their zero distribution.

## Contribution

It introduces a simple proof of a zero-free region for Rankin--Selberg L-functions, applicable to a broad class of automorphic representations, with minimal assumptions.

## Key findings

- Established a zero-free region in the t-aspect for Rankin--Selberg L-functions.
- Applicable to automorphic representations that are tempered outside a density-zero set.
- Simplified the proof technique for zero-free regions in this context.

## Abstract

We give a simple proof of a standard zero-free region in the $t$-aspect for the Rankin--Selberg $L$-function $L(s,\pi \times \widetilde{\pi})$ for any unitary cuspidal automorphic representation $\pi$ of $\mathrm{GL}_n(\mathbb{A}_F)$ that is tempered at every nonarchimedean place outside a set of Dirichlet density zero.