Lang-Trotter and Sato-Tate Distributions in Single and Double Parametric Families of Elliptic Curves

2014/04/01 by Min Sha, Sha, Min, Igor E. Shparlinski +1
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1404.0182

Abstract

We obtain new results concerning Lang-Trotter conjecture on Frobenius traces and Frobenius fields over single and double parametric families of elliptic curves. We also obtain similar results with respect to the Sato-Tate conjecture. In particular, we improve a result of A.C. Cojocaru and the second author (2008) towards the Lang-Trotter conjecture on average for polynomially parameterized families of elliptic curves when the parameter runs through a set of rational numbers of bounded height. Some of the families we consider are much thinner than the ones previously studied.

Citations

• The Lang-Trotter Conjecture on Average

Related

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• The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves
• On the Lang-Trotter conjecture for two elliptic curves
• The Sato--Tate Distribution in Families of Elliptic Curves with a Rational Parameter of Bounded Height
• A refined version of the Lang-Trotter Conjecture