An unconditional GLn large sieve

Jesse Thorner, Asif Zaman

Research output: Contribution to journalArticlepeer-review

Abstract

Let Fn be the set of cuspidal automorphic representations π of GLn over a number field with unitary central character. We prove two unconditional large sieve inequalities for the Hecke eigenvalues of π∈Fn, one on the integers and one on the primes. The second leads to the first unconditional zero density estimate for the family of L-functions L(s,π) associated to π∈Fn, which we make log-free. As an application of the zero density estimate, we prove a hybrid subconvexity bound for [Formula presented] for a density one subset of π∈Fn.

Original languageEnglish (US)
Article number107529
JournalAdvances in Mathematics
Volume378
DOIs
StatePublished - Feb 12 2021

Keywords

  • Automorphic representations
  • L-functions
  • Large sieve
  • Log-free zero density estimate
  • Selberg sieve
  • Subconvexity

ASJC Scopus subject areas

  • General Mathematics

Fingerprint

Dive into the research topics of 'An unconditional GLn large sieve'. Together they form a unique fingerprint.

Cite this