The first moment of central value of primitive quartic $L$-functions with fixed genus
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916938605658112 |
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| author | Hong, Ziwei |
| author_facet | Hong, Ziwei |
| contents | We investigate the mean value of the first moment of primitive quartic $L$-functions over $\mathbb{F}_q(T)$ in the non-Kummer setting. Specifically, we study the sum
\begin{equation*}
\sum_{\substack{χ primitive\ quartic\\ χ^2 primitive\\ genus(χ)=g}}L_q(\frac{1}{2}, χ),
\end{equation*} where $L_q(s,χ)$ denotes the $L$-function associated with primitive quartic character $χ$. Using double Dirichlet series, we derive an error term of size $q^{(\frac{3}{5}+\varepsilon)g}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14291 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The first moment of central value of primitive quartic $L$-functions with fixed genus Hong, Ziwei Number Theory We investigate the mean value of the first moment of primitive quartic $L$-functions over $\mathbb{F}_q(T)$ in the non-Kummer setting. Specifically, we study the sum \begin{equation*} \sum_{\substack{χ primitive\ quartic\\ χ^2 primitive\\ genus(χ)=g}}L_q(\frac{1}{2}, χ), \end{equation*} where $L_q(s,χ)$ denotes the $L$-function associated with primitive quartic character $χ$. Using double Dirichlet series, we derive an error term of size $q^{(\frac{3}{5}+\varepsilon)g}$. |
| title | The first moment of central value of primitive quartic $L$-functions with fixed genus |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.14291 |