Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Plane curves in boxes and equal sums of two powers   Given an absolutely irreducible ternary form $F$, the purpose of this paper
is to produce better upper bounds for the number of integer solutions to the
equation F=0, that are restricted to lie in very lopsided boxes. As an
application of the main result, a new paucity estimate is obtained for equal
sums of two like powers.

19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat