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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2501.11316 |
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| _version_ | 1866910790342148096 |
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| author | Ng, Iu-Iong Toma, Yuichiro |
| author_facet | Ng, Iu-Iong Toma, Yuichiro |
| contents | We deal with negative square moments of Dirichlet $L$-functions. Summing over characters modulo $q$, we obtain an asymptotic formula for the negative second moment of $L(1,χ)$ involving conductors. As an application, we give the improved lower bound on the success probability of the algorithm which recovers a short generator of the input generator of a principal ideal sampled from a specific Gaussian distribution in cyclotomic number fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11316 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mean square of inverses of Dirichlet $L$-functions involving conductors Ng, Iu-Iong Toma, Yuichiro Number Theory We deal with negative square moments of Dirichlet $L$-functions. Summing over characters modulo $q$, we obtain an asymptotic formula for the negative second moment of $L(1,χ)$ involving conductors. As an application, we give the improved lower bound on the success probability of the algorithm which recovers a short generator of the input generator of a principal ideal sampled from a specific Gaussian distribution in cyclotomic number fields. |
| title | Mean square of inverses of Dirichlet $L$-functions involving conductors |
| topic | Number Theory |
| url | https://arxiv.org/abs/2501.11316 |