Root numbers for twisted Fermat quotient curves
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911510212640768 |
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| author | Yanagihara, Ryosuke |
| author_facet | Yanagihara, Ryosuke |
| contents | Let $\ell$ be an odd prime, $N \geq 1$ be an integer, and $δ\geq 1$ be a $\ell^N$-th power free integer such that ${\rm ord}_{\ell}(δ) = 0$ or $\ell \nmid {\rm ord}_{\ell}(δ)$. In this paper, we give an explicit formula for the root number of the Hecke character associated with a certain quotient curve of the twisted Fermat curve $X^{\ell^N} + Y^{\ell^N} = δ$. This result gives a generalization of Stoll (2002) and Shu (2021). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22991 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Root numbers for twisted Fermat quotient curves Yanagihara, Ryosuke Number Theory Let $\ell$ be an odd prime, $N \geq 1$ be an integer, and $δ\geq 1$ be a $\ell^N$-th power free integer such that ${\rm ord}_{\ell}(δ) = 0$ or $\ell \nmid {\rm ord}_{\ell}(δ)$. In this paper, we give an explicit formula for the root number of the Hecke character associated with a certain quotient curve of the twisted Fermat curve $X^{\ell^N} + Y^{\ell^N} = δ$. This result gives a generalization of Stoll (2002) and Shu (2021). |
| title | Root numbers for twisted Fermat quotient curves |
| topic | Number Theory |
| url | https://arxiv.org/abs/2503.22991 |