Period four and real quadratic fields of class number one
type: Item
instance of: scholarly article
title: Period four and real quadratic fields of class number one
zbMATH Open document ID: 0705.11058
author: Richard A. Mollin
author: Hugh C. Williams
published in: Proceedings of the Japan Academy. Series A
publication date: 1989-01-01T00:00:00Z
review text: We quote the author's words: ``The purpose of this note is to provide criteria, in terms of prime-producing quadratic polynomials, for a real quadratic field \({\mathbb{Q}}(\sqrt{d})\) to have class number \(h(d)=1\), when the continued fraction expansion of \(\omega\) is (of period) 4 (where \(\omega =(1+\sqrt{d})/2\) if \(d\equiv 1 (\bmod 4)\) and \(\omega =\sqrt{d}\) if \(d\equiv 2,3 (mod 4))\).''
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 11N32
zbMATH DE Number: 4156568
zbMATH Keywords: class number one
zbMATH Keywords: Rabinowitsch criterion
zbMATH Keywords: prime-producing quadratic polynomials
zbMATH Keywords: real quadratic field
zbMATH Keywords: continued fraction expansion
reviewed by: K. Lakkis
MaRDI profile type: Publication
full work available at URL: pjaa.65.89
OpenAlex ID: W2092304547
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DOI: 10.3792/PJAA.65.89
description: scientific article; zbMATH DE number 4156568