Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The density of discriminants of quintic rings and fields   We determine, asymptotically, the number of quintic fields having bounded
discriminant. Specifically, we prove that the asymptotic number of quintic
fields having absolute discriminant at most X is a constant times X. In
contrast with the quartic case, we also show that a density of 100% of quintic
fields, when ordered by absolute discriminant, have Galois closure with full
Galois group $S_5$. The analogues of these results are also proven for orders
in quintic fields. Finally, we give an interpretation of the various constants
appearing in these theorems in terms of local masses of quintic rings and
fields.

13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an