Periodic twists of-Automorphic forms

Emmanuel Kowalski; Yongxiao Lin; Philippe Michel; Will Sawin

doi:10.1017/fms.2020.7

Periodic twists of-Automorphic forms

Emmanuel Kowalski, Yongxiao Lin, Philippe Michel, Will Sawin

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

5 Scopus citations

Abstract

We prove that sums of length about of Hecke eigenvalues of automorphic forms on do not correlate with-periodic functions with bounded Fourier transform. This generalizes the earlier results of Munshi and Holowinsky-Nelson, corresponding to multiplicative Dirichlet characters, and applies, in particular, to trace functions of small conductor modulo primes.

Original language	English (US)
Article number	7
Journal	Forum of Mathematics, Sigma
Volume	8
DOIs	https://doi.org/10.1017/fms.2020.7
State	Published - 2020
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Theoretical Computer Science
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Mathematics

Keywords

2010 Mathematics Subject Classification: 11F55 11M41 11L07 11T23 32N10

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10.1017/fms.2020.7

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title = "Periodic twists of-Automorphic forms",

abstract = "We prove that sums of length about of Hecke eigenvalues of automorphic forms on do not correlate with-periodic functions with bounded Fourier transform. This generalizes the earlier results of Munshi and Holowinsky-Nelson, corresponding to multiplicative Dirichlet characters, and applies, in particular, to trace functions of small conductor modulo primes.",

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T1 - Periodic twists of-Automorphic forms

AU - Kowalski, Emmanuel

AU - Lin, Yongxiao

AU - Michel, Philippe

AU - Sawin, Will

PY - 2020

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N2 - We prove that sums of length about of Hecke eigenvalues of automorphic forms on do not correlate with-periodic functions with bounded Fourier transform. This generalizes the earlier results of Munshi and Holowinsky-Nelson, corresponding to multiplicative Dirichlet characters, and applies, in particular, to trace functions of small conductor modulo primes.

AB - We prove that sums of length about of Hecke eigenvalues of automorphic forms on do not correlate with-periodic functions with bounded Fourier transform. This generalizes the earlier results of Munshi and Holowinsky-Nelson, corresponding to multiplicative Dirichlet characters, and applies, in particular, to trace functions of small conductor modulo primes.

KW - 2010 Mathematics Subject Classification: 11F55 11M41 11L07 11T23 32N10

UR - https://www.scopus.com/pages/publications/85082059290

UR - https://www.scopus.com/inward/citedby.url?scp=85082059290&partnerID=8YFLogxK

U2 - 10.1017/fms.2020.7

DO - 10.1017/fms.2020.7

M3 - Article

AN - SCOPUS:85082059290

SN - 2050-5094

VL - 8

JO - Forum of Mathematics, Sigma

JF - Forum of Mathematics, Sigma

M1 - 7

ER -

Periodic twists of-Automorphic forms

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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