Bounds for moments of twisted quadratic characters of prime modulus

2026/08/06 by Peng Gao, Yuetong Zhao
Mathematics · #math.NT

paper · pdf

23 pages

arxiv created 2026/08/06 · arxiv updated 2026/08/07

Abstract

We study, under the Generalized Riemann Hypothesis (GRH), the moments of sums of Fourier coefficients of a fixed holomorphic Hecke eigenform twisted by the quadratic character χ_8p, where p ranges over odd primes. We establish the correct order of magnitude for the unsmoothed m-th moment for all real m≥ 4, and a sharp upper bound of order XY^m/2 (log X)^m(m-3)/2 for the smoothed m-th moment for all integers m≥ 4. A matching lower bound for all even integers m≥ 4 shows that this bound is optimal.

Citations

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