Twisted second moment of primitive cubic L-functions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913914371964928 |
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| author | Hong, Ziwei Zheng, Zhiyong |
| author_facet | Hong, Ziwei Zheng, Zhiyong |
| contents | We investigate the mean value of the twisted second moment of primitive cubic $L$-functions over $\mathbb{F}_q(T)$ in the non-Kummer setting. Specifically, we study the sum \begin{equation*} \sum_{\substack{χ primitive\ cubic\\ genus(χ)=g}}χ(h_1)\barχ(h_2)|L_q(\frac{1}{2}, χ)|^2, \end{equation*} where $L_q(s,χ)$ denotes the $L$-function associated with primitive cubic character $χ$. Employing a double Dirichlet series approach, we establish an error term of size |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14656 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Twisted second moment of primitive cubic L-functions Hong, Ziwei Zheng, Zhiyong Number Theory 11M06, 11M41, 11N37, 11L05, 11L40 We investigate the mean value of the twisted second moment of primitive cubic $L$-functions over $\mathbb{F}_q(T)$ in the non-Kummer setting. Specifically, we study the sum \begin{equation*} \sum_{\substack{χ primitive\ cubic\\ genus(χ)=g}}χ(h_1)\barχ(h_2)|L_q(\frac{1}{2}, χ)|^2, \end{equation*} where $L_q(s,χ)$ denotes the $L$-function associated with primitive cubic character $χ$. Employing a double Dirichlet series approach, we establish an error term of size |
| title | Twisted second moment of primitive cubic L-functions |
| topic | Number Theory 11M06, 11M41, 11N37, 11L05, 11L40 |
| url | https://arxiv.org/abs/2506.14656 |