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arXiv · 1509.03009

The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves

Régis de la Bretèche·Min Sha·Igor E. Shparlinski·José Felipe Voloch
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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.

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Régis de la Bretèche, Min Sha, Igor E. Shparlinski, José Felipe Voloch. 2015-09-10. The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves. https://arxiv.org/abs/1509.03009

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