Regulator of the Hesse cubic curves and hypergeometric functions
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929317832818688 |
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| author | Nemoto, Yusuke |
| author_facet | Nemoto, Yusuke |
| contents | We construct some integral elements in the motivic cohomology of the Hesse cubic curves and express their regulators in terms of generalized hypergeometric functions and Kampé de Fériet hypergeometric functions. By using these hypergeometric expressions, we obtain numerical examples of the Bloch-Beilinson conjecture on special values of $L$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_12051 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Regulator of the Hesse cubic curves and hypergeometric functions Nemoto, Yusuke Number Theory 19F27, 33C20, 33C70 We construct some integral elements in the motivic cohomology of the Hesse cubic curves and express their regulators in terms of generalized hypergeometric functions and Kampé de Fériet hypergeometric functions. By using these hypergeometric expressions, we obtain numerical examples of the Bloch-Beilinson conjecture on special values of $L$-functions. |
| title | Regulator of the Hesse cubic curves and hypergeometric functions |
| topic | Number Theory 19F27, 33C20, 33C70 |
| url | https://arxiv.org/abs/2305.12051 |