High moments of random multiplicative functions twisted by Fourier coefficients of modular forms
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910279105773568 |
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| author | Gao, Peng Zhao, Liangyi |
| author_facet | Gao, Peng Zhao, Liangyi |
| contents | Let $λ(n)$ 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 $\E|\sum_{n \leq x} h(n)λ(n)|^{2q}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01514 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | High moments of random multiplicative functions twisted by Fourier coefficients of modular forms Gao, Peng Zhao, Liangyi Number Theory 11N37, 11N56, 11K65 Let $λ(n)$ 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 $\E|\sum_{n \leq x} h(n)λ(n)|^{2q}$ 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. |
| title | High moments of random multiplicative functions twisted by Fourier coefficients of modular forms |
| topic | Number Theory 11N37, 11N56, 11K65 |
| url | https://arxiv.org/abs/2606.01514 |