The Sato--Tate Distribution in Families of Elliptic Curves with a Rational Parameter of Bounded Height
Min Sha, Igor E. Shparlinski
TL;DR
This paper investigates the distribution of Frobenius angles in families of elliptic curves with rational parameters, providing new insights into the Sato--Tate conjecture for these parametric families.
Contribution
It presents novel results on the Sato--Tate distribution for elliptic curves with rational parameters of bounded height, expanding understanding in this area.
Findings
New distribution results for Frobenius angles in parametric elliptic curve families
Advances in understanding the Sato--Tate conjecture in a specific setting
Quantitative bounds related to the distribution of elliptic curve parameters
Abstract
We obtain new results concerning the Sato--Tate conjecture on the distribution of Frobenius angles over parametric families of elliptic curves with a rational parameter of bounded height.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Analytic Number Theory Research