The fourth moment of Dirichlet $L$-functions along a coset and the Weyl bound
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866913089435205632 |
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| author | Petrow, Ian Young, Matthew P. |
| author_facet | Petrow, Ian Young, Matthew P. |
| contents | We prove a Lindelöf-on-average upper bound for the fourth moment of Dirichlet $L$-functions of conductor $q$ along a coset of the subgroup of characters modulo $d$ when $q^*|d$, where $q^*$ is the least positive integer such that $q^2|(q^*)^3$. As a consequence, we finish the previous work of the authors and establish a Weyl-strength subconvex bound for all Dirichlet $L$-functions with no restrictions on the conductor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_10346 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The fourth moment of Dirichlet $L$-functions along a coset and the Weyl bound Petrow, Ian Young, Matthew P. Number Theory 11M06 (primary) 11F11 11F12 11F66 We prove a Lindelöf-on-average upper bound for the fourth moment of Dirichlet $L$-functions of conductor $q$ along a coset of the subgroup of characters modulo $d$ when $q^*|d$, where $q^*$ is the least positive integer such that $q^2|(q^*)^3$. As a consequence, we finish the previous work of the authors and establish a Weyl-strength subconvex bound for all Dirichlet $L$-functions with no restrictions on the conductor. |
| title | The fourth moment of Dirichlet $L$-functions along a coset and the Weyl bound |
| topic | Number Theory 11M06 (primary) 11F11 11F12 11F66 |
| url | https://arxiv.org/abs/1908.10346 |