The mollified fourth moment of Dirichlet $L$-functions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917048816238592 |
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| author | Gao, Peng Wu, Xiaosheng Zhao, Liangyi |
| author_facet | Gao, Peng Wu, Xiaosheng Zhao, Liangyi |
| contents | We prove an asymptotic formula with a power saving error term for the fourth moment of the family of Dirichlet $L$-functions to modulus $q$ mollified by a Dirichlet polynomial of length $q^{\frac1{22}-\ve}$, valid for all moduli $q\not\equiv2 \pmod 4$. This result was previously known only for restricted sets of moduli with smaller power savings. As a special case, when no Dirichlet polynomial is enclosed, this leads to a significant improvement on X. Wu's asymptotic evaluation of the fourth moment of Dirichlet $L$-functions at the cental point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24690 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The mollified fourth moment of Dirichlet $L$-functions Gao, Peng Wu, Xiaosheng Zhao, Liangyi Number Theory 11M06, 11F72 We prove an asymptotic formula with a power saving error term for the fourth moment of the family of Dirichlet $L$-functions to modulus $q$ mollified by a Dirichlet polynomial of length $q^{\frac1{22}-\ve}$, valid for all moduli $q\not\equiv2 \pmod 4$. This result was previously known only for restricted sets of moduli with smaller power savings. As a special case, when no Dirichlet polynomial is enclosed, this leads to a significant improvement on X. Wu's asymptotic evaluation of the fourth moment of Dirichlet $L$-functions at the cental point. |
| title | The mollified fourth moment of Dirichlet $L$-functions |
| topic | Number Theory 11M06, 11F72 |
| url | https://arxiv.org/abs/2509.24690 |