Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the $16$-rank of class groups of $\mathbb{Q}(\sqrt{-3p})$ for primes
  $p$ congruent to $1$ modulo $4$   For fixed $q\in\{3,7,11,19, 43,67,163\}$, we consider the density of primes
$p$ congruent to $1$ modulo $4$ such that the class group of the number field
$\mathbb{Q}(\sqrt{-qp})$ has order divisible by $16$. We show that this density
is equal to $1/8$, in line with a more general conjecture of Gerth.
Vinogradov's method is the key analytic tool for our work.

31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
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The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat