Moments of Artin-Schreier L-functions
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910564864753664 |
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| author | Florea, Alexandra Jones, Edna Lalin, Matilde |
| author_facet | Florea, Alexandra Jones, Edna Lalin, Matilde |
| contents | We compute moments of $L$-functions associated to the polynomial family of Artin--Schreier covers over $\mathbb{F}_q$, where $q$ is a power of a prime $p>2$, when the size of the finite field is fixed and the genus of the family goes to infinity. More specifically, we compute the $k^{\text{th}}$ moment for a large range of values of $k$, depending on the sizes of $p$ and $q$. We also compute the second moment in absolute value of the polynomial family, obtaining an exact formula with a lower order term, and confirming the unitary symmetry type of the family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_16487 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Moments of Artin-Schreier L-functions Florea, Alexandra Jones, Edna Lalin, Matilde Number Theory We compute moments of $L$-functions associated to the polynomial family of Artin--Schreier covers over $\mathbb{F}_q$, where $q$ is a power of a prime $p>2$, when the size of the finite field is fixed and the genus of the family goes to infinity. More specifically, we compute the $k^{\text{th}}$ moment for a large range of values of $k$, depending on the sizes of $p$ and $q$. We also compute the second moment in absolute value of the polynomial family, obtaining an exact formula with a lower order term, and confirming the unitary symmetry type of the family. |
| title | Moments of Artin-Schreier L-functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2306.16487 |