%0 Journal Article
%T Lang-Trotter and Sato-Tate Distributions in Single and Double Parametric Families of Elliptic Curves
%A Min Sha
%A Igor E. Shparlinski
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1404.0182v3