Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of equivalence classes of binary forms of given degree and
  given discriminant   We give an explicit upper bound for the number of equivalence classes of
binary forms with rational integral coefficients of given degree and given
discriminant, and with given splitting field. Further, we give an explicit
upper bound for the number of irreducible binary forms with rational integral
coefficients with given invariant order. Our bounds depend on as few parameters
as possible. For instance, we show that the number of equivalence classes of
irreducible binary forms with rational integral coefficients of degree r with
given invariant order has an upper bound depending only on r. We have proved
more general results for binary forms with coefficients in the ring of
S-integers of a number field.

11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th