Moments and One level density of sextic Hecke $L$-functions of $\mathbb{Q}(ω)$
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866914716241100800 |
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| author | Gao, Peng Zhao, Liangyi |
| author_facet | Gao, Peng Zhao, Liangyi |
| contents | In this paper, we study moments of central values of sextic Hecke $L$-functions of $\mathbb{Q}(ω)$ and one level density result for the low-lying zeros of sextic Hecke $L$-functions of $\mathbb{Q}(ω)$. As a corollary, we deduce that, assuming GRH, at least $2/45$ of the members of the sextic family do not vanish at $s=1/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_01885 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Moments and One level density of sextic Hecke $L$-functions of $\mathbb{Q}(ω)$ Gao, Peng Zhao, Liangyi Number Theory 11L05, 11L40, 11M06, 11M41, 11M50, 11R16 In this paper, we study moments of central values of sextic Hecke $L$-functions of $\mathbb{Q}(ω)$ and one level density result for the low-lying zeros of sextic Hecke $L$-functions of $\mathbb{Q}(ω)$. As a corollary, we deduce that, assuming GRH, at least $2/45$ of the members of the sextic family do not vanish at $s=1/2$. |
| title | Moments and One level density of sextic Hecke $L$-functions of $\mathbb{Q}(ω)$ |
| topic | Number Theory 11L05, 11L40, 11M06, 11M41, 11M50, 11R16 |
| url | https://arxiv.org/abs/2201.01885 |