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arXiv · 1409.6020

The Sato-Tate conjecture for a Picard curve with Complex Multiplication

Joan-C. Lario·Anna Somoza
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Abstract

Let C/Q be the genus 3 Picard curve given by the affine model y^3=x^4-x. In this paper we compute its Sato-Tate group, show the generalized Sato-Tate conjecture for C, and compute the statistical moments for the limiting distribution of the normalized local factors of C.

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Joan-C. Lario, Anna Somoza. 2014-09-21. The Sato-Tate conjecture for a Picard curve with Complex Multiplication. https://arxiv.org/abs/1409.6020

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