Regulators on some abelian coverings of $\mathbb{P}^1$ minus $n+2$ points
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917177888604160 |
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| author | Nemoto, Yusuke Yamauchi, Takuya |
| author_facet | Nemoto, Yusuke Yamauchi, Takuya |
| contents | In this paper, we construct certain rational or integral elements in the motivic cohomology of superelliptic curves which are quotient curves of abelian coverings of $\mathbb{P}^1$ minus $n+2$ points, and prove that these elements are non-trivial by expressing their regulators in terms of Appell-Lauricella hypergeometric functions. We also check that such elements are integral under a mild assumption. We also give various numerical examples for the Beilinson conjecture on special values of $L$-functions of the superelliptic curves by using hypergeometric expressions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_24607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regulators on some abelian coverings of $\mathbb{P}^1$ minus $n+2$ points Nemoto, Yusuke Yamauchi, Takuya Number Theory Algebraic Geometry 11F27, 11F67, 33C20, 33C99 In this paper, we construct certain rational or integral elements in the motivic cohomology of superelliptic curves which are quotient curves of abelian coverings of $\mathbb{P}^1$ minus $n+2$ points, and prove that these elements are non-trivial by expressing their regulators in terms of Appell-Lauricella hypergeometric functions. We also check that such elements are integral under a mild assumption. We also give various numerical examples for the Beilinson conjecture on special values of $L$-functions of the superelliptic curves by using hypergeometric expressions. |
| title | Regulators on some abelian coverings of $\mathbb{P}^1$ minus $n+2$ points |
| topic | Number Theory Algebraic Geometry 11F27, 11F67, 33C20, 33C99 |
| url | https://arxiv.org/abs/2512.24607 |