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arXiv · 2412.12515

Bounds for Moments of Twisted Fourier coefficients of Modular Forms

Peng Gao·Liangyi Zhao
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Abstract

We establish upper bounds for shifted moments of modular $L$-functions to a fixed modulus as well as quadratic twists of modular $L$-functions under the generalized Riemann hypothesis. Our results are then used to establish bounds for moments of sums involving with Fourier coefficients of a given modular form twisted by Dirichlet characters.

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Peng Gao, Liangyi Zhao. 2024-12-17. Bounds for Moments of Twisted Fourier coefficients of Modular Forms. https://arxiv.org/abs/2412.12515

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