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

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.

Keywords

• 11F55
• 11M41
• 11L07
• 11T23
• 32N10