On totally real cubic fields whose unit groups are of type \(\{\theta + r,\theta + s\}\)
type: Item
instance of: scholarly article
title: On totally real cubic fields whose unit groups are of type \(\{\theta + r,\theta + s\}\)
zbMATH Open document ID: 0933.11051
author: Kenji Minemura
published in: Proceedings of the Japan Academy. Series A
publication date: 2000-03-27T00:00:00Z
review text: The author determines all totally real cubic number fields possessing a system of fundamental units of the form \((\theta+r, \theta+s)\) for some \(r,s \in \mathbb Z\). For this, he uses the method of \textit{H. J. Godwin} [Proc. Camb. Philos. Soc. 56, 318-321 (1960; Zbl 0116.02802)] in the refined form given by \textit{H. Brunotte} and the reviewer [J. Number Theory 11, 552-559 (1979; Zbl 0408.12005)]. Using this method, he gives also a fresh proof of a result of H. Stender concerning units in fields generated by a root of \(x(x+s)(x+t)-1\) (Theorem 1). As H. J. Godwin observed, this proof can be simplified considerably attending the approximate size of the roots.
reviewed by: Franz Halter-Koch
Mathematics Subject Classification ID: 11R16
Mathematics Subject Classification ID: 11R80
Mathematics Subject Classification ID: 11R27
zbMATH DE Number: 1275059
zbMATH Keywords: totally real cubic number fields
zbMATH Keywords: fundamental units
MaRDI profile type: Publication
full work available at URL: pjaa.74.156
OpenAlex ID: W2019402351
cites work: Q5724850
cites work: Zur Einheitenberechnung in totalreellen kubischen Zahlkörpern nach Godwin
cites work: Einheiten für eine allgemeine Klasse total reeller algebraischer Zahlkörper.
cites work: Q3863959
cites work: On certain cubic fields. VI
cites work: Q3995206
cites work: Q3139838
DOI: 10.3792/PJAA.74.156
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description: scientific article; zbMATH DE number 1275059