A characterization of certain real quadratic fields
type: Item
instance of: scholarly article
title: A characterization of certain real quadratic fields
zbMATH Open document ID: 0593.12002
author: Ryuji Sasaki
published in: Proceedings of the Japan Academy. Series A
publication date: 1986-01-01T00:00:00Z
review text: Es seien \(d\) eine quadratfreie positive ganzrationale Zahl, \(\omega(d)=\sqrt{d}\) für \(d\equiv 2\text{ oder }3 \bmod 4\) und \(\omega(d)=(1+\sqrt{d})\) für \(d\equiv 1\bmod 4\), \(h(d)\) die Klassenzahl von \(\mathbb Q(\sqrt{d})\) und \(k(d)\) die Länge der Periode bei der Entwicklung von \(\omega(d)\) in einen Kettenbruch. In dieser Arbeit werden diejenigen reell-quadratischen Zahlkörper charakterisiert, für die \(h(d)=k(d)=1\) gilt.
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11A55
zbMATH DE Number: 3952890
zbMATH Keywords: real quadratic field
zbMATH Keywords: class number one
zbMATH Keywords: period length of continued fraction expansion
reviewed by: K. Lakkis
MaRDI profile type: Publication
full work available at URL: pjaa.62.97
OpenAlex ID: W2031663697
cites work: Q5816762
cites work: Q3252755
cites work: Q3941473
cites work: On a lower bound for the class number of an imaginary quadratic field
DOI: 10.3792/PJAA.62.97
description: scientific article; zbMATH DE number 3952890