The class number one problem for some totally complex quartic number fields
type: Item
instance of: scholarly article
title: The class number one problem for some totally complex quartic number fields
zbMATH Open document ID: 1167.11040
author: J. Martínez
published in: Journal of Number Theory
publication date: 2009-05-28T00:00:00Z
review text: Let \(K\) be a totally complex quartic field whose class number is equal to \(1\). The authors prove that there are 95 non-isomorphic fields \(K\) whose rings of algebraic integers are generated by an algebraic unit. Moreover, they prove Louboutin's conjecture according to which a totally complex quartic unit \(\varepsilon\) generally generates the unit group of the quartic order \(\mathbb Z[\varepsilon]\).
reviewed by: Abdelmalek Azizi
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 11R16
zbMATH DE Number: 5559083
zbMATH Keywords: quartic field
zbMATH Keywords: fundamental unit
zbMATH Keywords: class number
MaRDI profile type: Publication
full work available at URL: j.jnt.2009.01.022
OpenAlex ID: W2062788415
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DOI: 10.1016/J.JNT.2009.01.022
description: scientific article; zbMATH DE number 5559083