The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves
Number Theory
2018-03-08 v4
Abstract
We obtain new results concerning the Sato-Tate conjecture on the distribution of Frobenius traces over single and double parametric families of elliptic curves. We consider these curves for values of parameters having prescribed arithmetic structure: product sets, geometric progressions, and most significantly prime numbers. In particular, some families are much thinner than the ones previously studied.
Keywords
Cite
@article{arxiv.1509.03009,
title = {The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves},
author = {Régis de la Bretèche and Min Sha and Igor E. Shparlinski and José Felipe Voloch},
journal= {arXiv preprint arXiv:1509.03009},
year = {2018}
}