Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Density of rational points on diagonal quartic surfaces   Let a,b,c,d be nonzero rational numbers whose product is a square, and let V
be the diagonal quartic surface in PP^3 defined by ax^4+by^4+cz^4+dw^4=0. We
prove that if V contains a rational point that does not lie on any of the 48
lines on V or on any of the coordinate planes, then the set of rational points
on V is dense in both the Zariski topology and the real analytic topology.

20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics