PERIODIC TWISTS OF $\operatorname{GL}_{3}$-AUTOMORPHIC FORMS

PERIODIC TWISTS OF $\operatorname{GL}_{3}$-AUTOMORPHIC FORMS

We prove that sums of length about $q^{3/2}$ of Hecke eigenvalues of automorphic forms on $\operatorname{SL}_{3}(\mathbf{Z})$ do not correlate with $q$-periodic functions with bounded Fourier transform. This generalizes the earlier results of Munshi and Holowinsky–Nelson, corresponding to multiplica...

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Bibliographic Details
Main Authors: EMMANUEL KOWALSKI, YONGXIAO LIN, PHILIPPE MICHEL, WILL SAWIN
Format: Article
Language:English
Published: Cambridge University Press 2020-01-01
Series:Forum of Mathematics, Sigma
Subjects:
11F55
11M41
11L07
11T23
32N10
Online Access:https://www.cambridge.org/core/product/identifier/S2050509420000079/type/journal_article
Description
Summary:We prove that sums of length about $q^{3/2}$ of Hecke eigenvalues of automorphic forms on $\operatorname{SL}_{3}(\mathbf{Z})$ do not correlate with $q$-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.
ISSN:2050-5094

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