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.
Categories: math.NT