Bounds for Moments of Dirichlet $L$-functions of fixed modulus on the critical line
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909623009673216 |
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| author | Gao, Peng Zhao, Liangyi |
| author_facet | Gao, Peng Zhao, Liangyi |
| contents | We study the $2k$-th moment of the family of Dirichlet $L$-functions to a fixed prime modulus on the critical line and establish sharp lower bounds for all real $k \geq 0$ and sharp upper bounds for $k$ in the range $0 \leq k \leq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19375 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounds for Moments of Dirichlet $L$-functions of fixed modulus on the critical line Gao, Peng Zhao, Liangyi Number Theory 11M06 We study the $2k$-th moment of the family of Dirichlet $L$-functions to a fixed prime modulus on the critical line and establish sharp lower bounds for all real $k \geq 0$ and sharp upper bounds for $k$ in the range $0 \leq k \leq 1$. |
| title | Bounds for Moments of Dirichlet $L$-functions of fixed modulus on the critical line |
| topic | Number Theory 11M06 |
| url | https://arxiv.org/abs/2505.19375 |