Twisted second moment of modular $L$-functions to a fixed modulus
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909563322630144 |
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| author | Gao, Peng Zhao, Liangyi |
| author_facet | Gao, Peng Zhao, Liangyi |
| contents | We study asymptotically the twisted second moment of the family of modular $L$-functions to a fixed modulus. As an application, we establish sharp lower bounds for all real $k \geq 0$ and sharp upper bounds for $k$ in the range $0 \leq k \leq 1$ for the $2k$-th moment of these $L$-functions on the critical line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Twisted second moment of modular $L$-functions to a fixed modulus Gao, Peng Zhao, Liangyi Number Theory 11M06 We study asymptotically the twisted second moment of the family of modular $L$-functions to a fixed modulus. As an application, we establish sharp lower bounds for all real $k \geq 0$ and sharp upper bounds for $k$ in the range $0 \leq k \leq 1$ for the $2k$-th moment of these $L$-functions on the critical line. |
| title | Twisted second moment of modular $L$-functions to a fixed modulus |
| topic | Number Theory 11M06 |
| url | https://arxiv.org/abs/2504.02225 |