Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hilbert genus fields of some number fields with high degrees   The aim of this paper is to give some properties of Hilbert genus fields and
  construct the Hilbert genus fields of the fields
$L_{m,d}:=\mathbb{Q}(\zeta_{2^m},\sqrt{d})$, where $m\geq 3$ is a positive
integer and $d$ is a square-free integer whose prime divisors are congruent to
$\pm 3\pmod 8$ or $9\pmod{16}$.

22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom