First moment of central values of Hecke $L$-functions with Fixed Order Characters
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866909938891096064 |
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| author | Gao, Peng Zhao, Liangyi |
| author_facet | Gao, Peng Zhao, Liangyi |
| contents | We evaluate asymptotically the smoothed first moment of central values of families of quadratic, cubic, quartic and sextic Hecke $L$-functions over various imaginary quadratic number fields of class number one, using the method of double Dirichlet series. In particular, we obtain asymptotic formulas for the quadratic families with error terms of size $O(X^{1/4+\varepsilon})$ under the generalized Riemann hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10726 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | First moment of central values of Hecke $L$-functions with Fixed Order Characters Gao, Peng Zhao, Liangyi Number Theory 11M06, 11M41, 11N37, 11L05, 11L40, 11R11 We evaluate asymptotically the smoothed first moment of central values of families of quadratic, cubic, quartic and sextic Hecke $L$-functions over various imaginary quadratic number fields of class number one, using the method of double Dirichlet series. In particular, we obtain asymptotic formulas for the quadratic families with error terms of size $O(X^{1/4+\varepsilon})$ under the generalized Riemann hypothesis. |
| title | First moment of central values of Hecke $L$-functions with Fixed Order Characters |
| topic | Number Theory 11M06, 11M41, 11N37, 11L05, 11L40, 11R11 |
| url | https://arxiv.org/abs/2306.10726 |