A note on simple zeros related to Dedekind zeta functions
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909160195489792 |
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| author | Zhang, Wei |
| author_facet | Zhang, Wei |
| contents | We give a conditional lower bound on the number of non-trivial simple zeros for the Dedekind zeta function $ζ_{K}(s)$, where $K$ is a quadratic number field. The conditional result is given by assuming a Lindelöf on average (in the $L^{6}$ sense) for both $ζ(s)$ and $L(s,χ)$, which can be seen as a stronger version of Conrey-Gonek-Ghosh's \cite{c} conditional result. This improves upon the work of Wu and Zhao \cite{Zhao}, who had a similar result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07360 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on simple zeros related to Dedekind zeta functions Zhang, Wei Number Theory 11M06, 11M41 We give a conditional lower bound on the number of non-trivial simple zeros for the Dedekind zeta function $ζ_{K}(s)$, where $K$ is a quadratic number field. The conditional result is given by assuming a Lindelöf on average (in the $L^{6}$ sense) for both $ζ(s)$ and $L(s,χ)$, which can be seen as a stronger version of Conrey-Gonek-Ghosh's \cite{c} conditional result. This improves upon the work of Wu and Zhao \cite{Zhao}, who had a similar result. |
| title | A note on simple zeros related to Dedekind zeta functions |
| topic | Number Theory 11M06, 11M41 |
| url | https://arxiv.org/abs/2310.07360 |