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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2511.02344 |
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| _version_ | 1866911248118972416 |
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| author | Gao, Peng Zhao, Liangyi |
| author_facet | Gao, Peng Zhao, Liangyi |
| contents | For any large prime $q$, $x \leq 1$ and any real $k\geq 2$, we prove a lower bound for the following $2k$-th moment
\begin{equation*}
\sum_{\substack{χ\in X_q^*}} \Big| \sum_{n\leq x} χ(n)λ(n)\Big|^{2k}, \end{equation*}
where $X_q^*$ denotes the set of primitive Dirichlet characters modulo $q$ and $λ(n)$ the Fourier coefficients of a fixed modular form. The bound we obtain is sharp up to a constant factor under the generalized Riemann Hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02344 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lower Bounds on High Moments of Twisted Fourier coefficients of Modular Forms Gao, Peng Zhao, Liangyi Number Theory 11L40, 11M06 For any large prime $q$, $x \leq 1$ and any real $k\geq 2$, we prove a lower bound for the following $2k$-th moment \begin{equation*} \sum_{\substack{χ\in X_q^*}} \Big| \sum_{n\leq x} χ(n)λ(n)\Big|^{2k}, \end{equation*} where $X_q^*$ denotes the set of primitive Dirichlet characters modulo $q$ and $λ(n)$ the Fourier coefficients of a fixed modular form. The bound we obtain is sharp up to a constant factor under the generalized Riemann Hypothesis. |
| title | Lower Bounds on High Moments of Twisted Fourier coefficients of Modular Forms |
| topic | Number Theory 11L40, 11M06 |
| url | https://arxiv.org/abs/2511.02344 |