Mollified moments of quadratic Dirichlet $L$-functions over function fields
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866915042750889984 |
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| author | Andrade, Julio C. Best, Christopher G. |
| author_facet | Andrade, Julio C. Best, Christopher G. |
| contents | We compute asymptotic formulae for the mollified first and second moments for the family of quadratic Dirichlet $L$-functions in the function field setting. As an application, we obtain non-vanishing results for the derivatives of the completed $L$-functions $Λ(s,χ_D)$ at the central point $s=1/2$. In particular, we show that the proportion of $Λ^{(2k)}(\frac{1}{2},χ_D) \neq 0$ is $1+O(k^{-2})$ as $k \to \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_11005 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Mollified moments of quadratic Dirichlet $L$-functions over function fields Andrade, Julio C. Best, Christopher G. Number Theory We compute asymptotic formulae for the mollified first and second moments for the family of quadratic Dirichlet $L$-functions in the function field setting. As an application, we obtain non-vanishing results for the derivatives of the completed $L$-functions $Λ(s,χ_D)$ at the central point $s=1/2$. In particular, we show that the proportion of $Λ^{(2k)}(\frac{1}{2},χ_D) \neq 0$ is $1+O(k^{-2})$ as $k \to \infty$. |
| title | Mollified moments of quadratic Dirichlet $L$-functions over function fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2201.11005 |