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

Márton Erdélyi

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arXiv · 1609.06066

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

Márton Erdélyi

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Abstract

Let $K$ be a global field of finite characteristic $p\geq2$, and let $E/K$ be a non-isotrivial elliptic curve. We give an asympotoic formula of the number of places $\nu$ for which the reduction of $E$ at $\nu$ is a cyclic group. Moreover we determine when the Dirichlet density of those places is 0.

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Márton Erdélyi. 2016-09-20. The distribution and density of cyclic groups of the reductions of an elliptic curve over a function field. https://arxiv.org/abs/1609.06066

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