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arXiv · 1901.10656

The distribution of multiples of real points on an elliptic curve

Alex Cowan
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Abstract

Given an elliptic curve $E$ and a point $P$ in $E(\mathbb{R})$, we investigate the distribution of the points $nP$ as $n$ varies over the integers, giving bounds on the $x$ and $y$ coordinates of $nP$ and determining the natural density of integers $n$ for which $nP$ lies in an arbitrary open subset of $\mathbb{R}^2$. Our proofs rely on a connection to classical topics in the theory of Diophantine approximation.

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Alex Cowan. 2019-01-30. The distribution of multiples of real points on an elliptic curve. https://doi.org/10.1016/j.jnt.2019.12.010

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