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arXiv · 1404.0182

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

Min Sha·Igor E. Shparlinski
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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.

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Min Sha, Igor E. Shparlinski. 2014-04-01. Lang-Trotter and Sato-Tate Distributions in Single and Double Parametric Families of Elliptic Curves. https://arxiv.org/abs/1404.0182

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