Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The density of rational points in curves and surfaces   Let $X$ be an algebraic variety, defined over the rationals. This paper gives
upper bounds for the number of rational points on $X$, with height at most $B$,
for the case in which $X$ is a curve or a surface. In the latter case one
excludes from the counting function those points that lie on lines in the
surface. The bounds are uniform for all $X$ of a given degree. They are best
possible in the case of curves. As an application it is shown that if $F$ is an
irreducible binary form of degree 3 or more then almost all integers
represented by $F$ have essentially one such representation.

26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int