Murmurations and Sato-Tate Conjectures for High Rank Zetas of Elliptic Curves
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909338569801728 |
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| author | Shi, Zhan Weng, Lin |
| author_facet | Shi, Zhan Weng, Lin |
| contents | For elliptic curves over rationals, there are a well-known conjecture of Sato-Tate and a new computational guided murmuration phenomenon, for which the abelian Hasse-Weil zeta functions are used. In this paper, we show that both the murmurations and the Sato-Tate conjecture stand equally well for non-abelian high rank zeta functions of the p-reductions of elliptic curves over rationals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04952 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Murmurations and Sato-Tate Conjectures for High Rank Zetas of Elliptic Curves Shi, Zhan Weng, Lin Number Theory Algebraic Geometry For elliptic curves over rationals, there are a well-known conjecture of Sato-Tate and a new computational guided murmuration phenomenon, for which the abelian Hasse-Weil zeta functions are used. In this paper, we show that both the murmurations and the Sato-Tate conjecture stand equally well for non-abelian high rank zeta functions of the p-reductions of elliptic curves over rationals. |
| title | Murmurations and Sato-Tate Conjectures for High Rank Zetas of Elliptic Curves |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2410.04952 |