Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On small discriminants of number fields of degree 8 and 9   We classify all the number fields with signature (4,2), (6,1), (1,4) and
(3,3) having discriminant lower than a specific upper bound. This completes the
search for minimum discriminants for fields of degree 8 and continues it in the
degree 9 case. We recall the theoretical tools and the algorithmic steps upon
which our procedure is based, then we focus on the novelties due to a new
implementation of this process on the computer algebra system PARI/GP; finally,
we make some remarks about the final results, among which the existence of a
number field with signature $(3,3)$ and small discriminant which was not
previously known.

22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con