Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910296819367936 |
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| author | Gao, Peng Zhao, Liangyi |
| author_facet | Gao, Peng Zhao, Liangyi |
| contents | We develope the $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic Hecke $L$-functions in the Gaussian field using multiple Dirichlet series under the generalized Riemann hypothesis. We also obtain an asymptotical formula for the first moment of central values of the same family of $L$-functions, obtaining an error term of size $O(X^{1/2+\varepsilon})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_08840 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field Gao, Peng Zhao, Liangyi Number Theory 11M06, 11M41 We develope the $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic Hecke $L$-functions in the Gaussian field using multiple Dirichlet series under the generalized Riemann hypothesis. We also obtain an asymptotical formula for the first moment of central values of the same family of $L$-functions, obtaining an error term of size $O(X^{1/2+\varepsilon})$. |
| title | Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field |
| topic | Number Theory 11M06, 11M41 |
| url | https://arxiv.org/abs/2210.08840 |