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

Peter Humphries

doi:10.1007/s00209-018-2136-8

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

Number Theory 2019-07-24 v3

Authors: Peter Humphries

View on arXiv ↗ PDF ↗ DOI ↗

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.

Keywords

Rankin-Selberg L-functions zero-free region sieve theory cuspidal automorphic representation Dirichlet density

Cite

@article{arxiv.1703.05450,
  title  = {Standard Zero-Free Regions for Rankin--Selberg L-Functions via Sieve Theory},
  author = {Peter Humphries},
  journal= {arXiv preprint arXiv:1703.05450},
  year   = {2019}
}

Comments

16 pages. With an appendix by Farrell Brumley

Related papers

View all related →