The distribution of multiples of real points on an elliptic curve

Abstract

Given an elliptic curve E and a point P in E(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 R2. Our proofs rely on a connection to classical topics in the theory of Diophantine approximation.