Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The distribution of multiples of real points on an elliptic curve   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.

24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess