Ratios conjecture of quartic $L$-functions of prime moduli
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912935294533632 |
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| author | Gao, Peng Zhao, Liangyi |
| author_facet | Gao, Peng Zhao, Liangyi |
| contents | We apply the method of multiple Dirichlet series to develop $L$-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for the family of quartic Hecke $L$-functions of prime moduli over the Gaussian field under the generalized Riemann hypothesis. As consequences, 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_2402_17198 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ratios conjecture of quartic $L$-functions of prime moduli Gao, Peng Zhao, Liangyi Number Theory 11M06, 11M41 We apply the method of multiple Dirichlet series to develop $L$-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for the family of quartic Hecke $L$-functions of prime moduli over the Gaussian field under the generalized Riemann hypothesis. As consequences, 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 quartic $L$-functions of prime moduli |
| topic | Number Theory 11M06, 11M41 |
| url | https://arxiv.org/abs/2402.17198 |