Certain quartic fields with small regulators
type: Item
instance of: scholarly article
title: Certain quartic fields with small regulators
zbMATH Open document ID: 0847.11057
author: Ken Nakamula
published in: Journal of Number Theory
publication date: 1996-10-13T00:00:00Z
review text: The author gives explicit lower bounds of the regulators \(R_K\) of quartic fields \(K\) in terms of the discriminant of \(K\) and his results cover quartic fields of unit ranks 1, 2 and 3. Using the fields \(\mathbb{Q}(\omega)\), where \(\omega\) is a root of \(x^4- sx^3+ (t+ 2u) x^2- usx+ 1\), the author shows that his estimates are in a sense best possible by exhibiting for certain values of \(s\), \(t\) and \(u\) fundamental systems of units. The above polynomial looks like a generalization of the polynomial \(x^4- sx^3+ rx^2- usx+ 1\), with \(r= ((s^2- mz^2)/4)+ zu\), considered by \textit{G. Gras} [Publ. Math. Fac. Sci. Besançon, Theor. Nombres, Exp. 5 (1979; Zbl 0472.12009)]. This paper will certainly prove interesting to number theorists involved with units (and class numbers).
reviewed by: Claude Levesque
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 11R16
Mathematics Subject Classification ID: 11R29
zbMATH DE Number: 874227
zbMATH Keywords: lower bounds of the regulators of quartic fields
zbMATH Keywords: fundamental systems of units
MaRDI profile type: Publication
full work available at URL: jnth.1996.0031
OpenAlex ID: W2041669931
DOI: 10.1006/JNTH.1996.0031
description: scientific article; zbMATH DE number 874227