Ratios conjecture of cubic $L$-functions of prime moduli
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913938480824320 |
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| author | Gao, Peng Zhao, Liangyi |
| author_facet | Gao, Peng Zhao, Liangyi |
| contents | We develop $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of cubic Hecke $L$-functions of prime moduli over the Eisenstein field using multiple Dirichlet series under the generalized Riemann hypothesis. As applications, we evaluate asymptotically the first moment of central values as well as the one-level density of the same family of $L$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_08626 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ratios conjecture of cubic $L$-functions of prime moduli Gao, Peng Zhao, Liangyi Number Theory 11M06, 11M41 We develop $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of cubic Hecke $L$-functions of prime moduli over the Eisenstein field using multiple Dirichlet series under the generalized Riemann hypothesis. As applications, we evaluate asymptotically the first moment of central values as well as the one-level density of the same family of $L$-functions. |
| title | Ratios conjecture of cubic $L$-functions of prime moduli |
| topic | Number Theory 11M06, 11M41 |
| url | https://arxiv.org/abs/2311.08626 |