Periodic twists of GL3-automorphic forms
Abstract
We prove that sums of length about q3/2 of Hecke eigenvalues of automorphic forms on SL3() 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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