Skip to main content

The density of discriminants of quintic rings and fields

Author(s): Bhargava, Manjul

To refer to this page use:
Abstract: 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.
Publication Date: 2010
Citation: Bhargava, Manjul. “The Density of Discriminants of Quintic Rings and Fields.” Annals of Mathematics, vol. 172, no. 3, 2010, pp. 1559–91. JSTOR, Accessed 18 Feb. 2024.
Type of Material: Journal Article
Journal/Proceeding Title: Annals of Mathematics
Version: Author's manuscript

Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.