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arXiv · 1905.05080

Periodic twists of $GL_3$-automorphic forms

Emmanuel Kowalski·Yongxiao Lin·Philippe Michel·Will Sawin
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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.

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Emmanuel Kowalski, Yongxiao Lin, Philippe Michel, Will Sawin. 2019-05-13. Periodic twists of $GL_3$-automorphic forms. https://arxiv.org/abs/1905.05080

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