An unconditional GLn large sieve

Jesse Thorner; Asif Zaman

doi:10.1016/j.aim.2020.107529

An unconditional GL_n large sieve

Jesse Thorner, Asif Zaman

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let F_n be the set of cuspidal automorphic representations π of GL_n over a number field with unitary central character. We prove two unconditional large sieve inequalities for the Hecke eigenvalues of π∈F_n, 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∈F_n, 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∈F_n.

Original language	English (US)
Article number	107529
Journal	Advances in Mathematics
Volume	378
DOIs	https://doi.org/10.1016/j.aim.2020.107529
State	Published - Feb 12 2021

Keywords

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

ASJC Scopus subject areas

General Mathematics

Online availability

10.1016/j.aim.2020.107529

Library availability

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Cite this

@article{2d2e29d94adf4aba875bbd88593304b8,

title = "An unconditional GLn large sieve",

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.",

keywords = "Automorphic representations, L-functions, Large sieve, Log-free zero density estimate, Selberg sieve, Subconvexity",

author = "Jesse Thorner and Asif Zaman",

note = "Funding Information: We thank Nickolas Andersen, Farrell Brumley, and Peter Humphries for helpful discussions. We especially thank Kannan Soundararajan, who showed us how our idea for Theorem 1.1 leads to Proposition 3.1, and the anonymous referees for their numerous suggestions and comments. Work on this paper began while the authors were postdoctoral researchers at Stanford University. Jesse Thorner was partially supported by an NSF Postdoctoral Fellowship. Asif Zaman was partially supported by an NSERC fellowship. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2021",

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doi = "10.1016/j.aim.2020.107529",

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T1 - An unconditional GLn large sieve

AU - Thorner, Jesse

AU - Zaman, Asif

N1 - Funding Information: We thank Nickolas Andersen, Farrell Brumley, and Peter Humphries for helpful discussions. We especially thank Kannan Soundararajan, who showed us how our idea for Theorem 1.1 leads to Proposition 3.1, and the anonymous referees for their numerous suggestions and comments. Work on this paper began while the authors were postdoctoral researchers at Stanford University. Jesse Thorner was partially supported by an NSF Postdoctoral Fellowship. Asif Zaman was partially supported by an NSERC fellowship. Publisher Copyright: © 2020 Elsevier Inc.

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Y1 - 2021/2/12

N2 - 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.

AB - 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.

KW - Automorphic representations

KW - L-functions

KW - Large sieve

KW - Log-free zero density estimate

KW - Selberg sieve

KW - Subconvexity

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