The Sato-Tate conjecture for a Picard curve with Complex Multiplication
Number Theory
2014-10-02 v2
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.
Cite
@article{arxiv.1409.6020,
title = {The Sato-Tate conjecture for a Picard curve with Complex Multiplication},
author = {Joan-C. Lario and Anna Somoza},
journal= {arXiv preprint arXiv:1409.6020},
year = {2014}
}