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arXiv · 2509.20085

Bounds for integral moments of quadratic twists of Fourier coefficients of modular forms

Peng Gao·Yuetong Zhao
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Abstract

In this paper, we obtain under the assumption of the Generalized Riemann Hypothesis upper bounds for all high integral moments of sums of Fourier coefficients of a given modular form twisted by quadratic Dirichlet characters. We show the bounds are optimal by establishing unconditionally the corresponding lower bounds for all even integer moments.

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Peng Gao, Yuetong Zhao. 2025-09-24. Bounds for integral moments of quadratic twists of Fourier coefficients of modular forms. https://arxiv.org/abs/2509.20085

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