Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Half-integral weight modular forms and real quadratic $p$-rational
  fields   Using half-integral weight modular forms we give a criterion for the
existence of real quadratic $p$-rational fields. For $p=5$ we prove the
existence of infinitely many real quadratic $p$-rational fields.

9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph