English

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}
}