Low moments of random multiplicative functions twisted by Fourier coefficients of modular forms
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914464858636288 |
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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 the order of magnitude of \[ \E|\sum_{n \leq x} h(n)λ(n)|^{2q} \] for real $x$, $q$ with $0 \leq q \leq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09968 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Low moments of random multiplicative functions twisted by Fourier coefficients of modular forms Gao, Peng Zhao, Liangyi Number Theory 11N37, 11L40, 11K65, 60G15, 60G57 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 the order of magnitude of \[ \E|\sum_{n \leq x} h(n)λ(n)|^{2q} \] for real $x$, $q$ with $0 \leq q \leq 1$. |
| title | Low moments of random multiplicative functions twisted by Fourier coefficients of modular forms |
| topic | Number Theory 11N37, 11L40, 11K65, 60G15, 60G57 |
| url | https://arxiv.org/abs/2604.09968 |