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PERIODIC TWISTS OF $\operatorname{GL}_{3}$-AUTOMORPHIC FORMS
Published online by Cambridge University Press: 12 March 2020
Abstract
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.
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- Number Theory
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- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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- © The Author(s) 2020
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