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arXiv · 2606.01514

High moments of random multiplicative functions twisted by Fourier coefficients of modular forms

Peng Gao·Liangyi Zhao
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Abstract

Let $\lambda(n)$ denote the Fourier coefficients of a fixed modular form and $h(n)$ a Steinhaus or Rademacher random multiplicative function. In this paper, we determine, under the generalized Riemann hypothesis, the order of magnitude of $\E|\sum_{n \leq x} h(n)\lambda(n)|^{2q}$ up to factors of size $e^{O(q^2)}$, for all real $x, q$ with $1 \leq q \leq c\log x/\log\log x $ and $c>0$ a small constant.

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Peng Gao, Liangyi Zhao. 2026-06-01. High moments of random multiplicative functions twisted by Fourier coefficients of modular forms. https://arxiv.org/abs/2606.01514

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