Periodic twists of $GL_3$-automorphic forms

Emmanuel Kowalski; Yongxiao Lin; Philippe Michel; Will Sawin

Periodic twists of $GL_3$-automorphic forms

Number Theory 2019-12-24 v3

Authors: Emmanuel Kowalski , Yongxiao Lin , Philippe Michel , Will Sawin

Abstract

We prove that sums of length about $q^{3/2}$ of Hecke eigenvalues of automorphic forms on $SL_3(\Zz)$ 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.

Keywords

automorphic forms hecke eigenvalues periodic twists dirichlet characters trace functions sl_3

Cite

@article{arxiv.1905.05080,
  title  = {Periodic twists of $GL_3$-automorphic forms},
  author = {Emmanuel Kowalski and Yongxiao Lin and Philippe Michel and Will Sawin},
  journal= {arXiv preprint arXiv:1905.05080},
  year   = {2019}
}

Comments

modified following suggestions and comments from the referees; added Remark 1.8

Periodic twists of $GL_3$-automorphic forms

Abstract

Keywords

Cite

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