Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the $4$-rank of class groups of Dirichlet biquadratic fields   We show that for $100\%$ of the odd, squarefree integers $n > 0$ the $4$-rank
of $\text{Cl}(\mathbb{Q}(i, \sqrt{n}))$ is equal to $\omega_3(n) - 1$, where
$\omega_3$ is the number of prime divisors of $n$ that are $3$ modulo $4$.

10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th