Ratios conjecture of quadratic Hecke $L$-functions of prime-related moduli
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914748009807872 |
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| author | Gao, Peng Zhao, Liangyi |
| author_facet | Gao, Peng Zhao, Liangyi |
| contents | Using the method of multiple Dirichlet series, we develop L-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for quadratic families of Dirichlet and Hecke L-functions of primerelated moduli of imaginary quadratic number fields of class number one under the generalized Riemann hypothesis. As corollaries, we evaluate asymptotically the first moment of central values as well as the one-level density of the families of L-functions under consideration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05081 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ratios conjecture of quadratic Hecke $L$-functions of prime-related moduli Gao, Peng Zhao, Liangyi Number Theory 11M06, 11M41 Using the method of multiple Dirichlet series, we develop L-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for quadratic families of Dirichlet and Hecke L-functions of primerelated moduli of imaginary quadratic number fields of class number one under the generalized Riemann hypothesis. As corollaries, we evaluate asymptotically the first moment of central values as well as the one-level density of the families of L-functions under consideration. |
| title | Ratios conjecture of quadratic Hecke $L$-functions of prime-related moduli |
| topic | Number Theory 11M06, 11M41 |
| url | https://arxiv.org/abs/2404.05081 |