Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting integral points on indefinite ternary quadratic equations over
  number fields   We study an asymptotic formula for counting integral points over an equation
defined by a non-degenerated indefinite integral ternary quadratic form $f$
representing a non-zero integer $a$ such that $-a\cdot det(f)$ is square over a
number field. In particular, we prove that the finite part of this asymptotic
formula is given by the product of local density times $1-p^{-1}$ over all
finite primes $p$ over $\Bbb Z$.

29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex