an:06860518
Zbl 1440.11100
Lario, Joan-Carles; Somoza, Anna
The Sato-Tate conjecture for a Picard curve with complex multiplication (with an appendix by Francesc Fit??)
EN
Lario, Joan-Carles (ed.) et al., Number theory related to modular curves: Momose memorial volume. Proceedings of the Barcelona-Boston-Tokyo Number Theory Seminar in memory of Fumiyuki Momose, Barcelona, Spain, May 21--23, 2012. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 701, 151-165 (2018).
2018
a
11G10 11G15 11G30 11G40
Sato-Tate conjecture; Picard curve
Summary: Let \(C/\mathbb {Q}\) 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 \(C\).
For the entire collection see [Zbl 1384.11002].