The second moment of cubic Dirichlet L-functions over function fields
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912394400235520 |
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| author | Goel, Shivani Ray, Anwesh |
| author_facet | Goel, Shivani Ray, Anwesh |
| contents | In this article, we study the second moment of cubic Dirichlet L-functions at the central point $s=1/2$ over the rational function field $\mathbb{F}_q(T)$, where $q$ is a power of an odd prime satisfying $q \equiv 2 \pmod{3}$. Our result extends prior work of David, Florea and Lalin, who obtained an asymptotic formula for the first moment. Our approach relies on analytic techniques (Perron's formula, approximate functional equation, etc), adapted to the function field context. A key step in the construction is to relate second moment to certain averages of Gauss sums, which are estimated in loc. cit. using results of Kubota and Hoffstein. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_12015 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The second moment of cubic Dirichlet L-functions over function fields Goel, Shivani Ray, Anwesh Number Theory 11R59, 11M38, 11R58 In this article, we study the second moment of cubic Dirichlet L-functions at the central point $s=1/2$ over the rational function field $\mathbb{F}_q(T)$, where $q$ is a power of an odd prime satisfying $q \equiv 2 \pmod{3}$. Our result extends prior work of David, Florea and Lalin, who obtained an asymptotic formula for the first moment. Our approach relies on analytic techniques (Perron's formula, approximate functional equation, etc), adapted to the function field context. A key step in the construction is to relate second moment to certain averages of Gauss sums, which are estimated in loc. cit. using results of Kubota and Hoffstein. |
| title | The second moment of cubic Dirichlet L-functions over function fields |
| topic | Number Theory 11R59, 11M38, 11R58 |
| url | https://arxiv.org/abs/2505.12015 |