Gardado en:
| Main Authors: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Subjects: | |
| Acceso en liña: | https://arxiv.org/abs/2201.11005 |
| Tags: |
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Table of 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 $k \to \infty$.