The distribution and density of cyclic groups of the reductions of an elliptic curve over a function field

Márton Erdélyi

paper

The distribution and density of cyclic groups of the reductions of an elliptic curve over a function field

arXiv:1609.06066

Abstract

Let $K$ be a global field of finite characteristic $p \geq 2$ , and let $E / K$ be a non-isotrivial elliptic curve. We give an asympotoic formula of the number of places $ν$ for which the reduction of $E$ at $ν$ is a cyclic group. Moreover we determine when the Dirichlet density of those places is 0.

9 pages. Comments welcome