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arXiv · 2410.04952

Murmurations and Sato-Tate Conjectures for High Rank Zetas of Elliptic Curves

Zhan Shi·Lin Weng
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Abstract

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.

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Zhan Shi, Lin Weng. 2024-10-07. Murmurations and Sato-Tate Conjectures for High Rank Zetas of Elliptic Curves. https://arxiv.org/abs/2410.04952

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