Class number one criteria for real quadratic fields. II
type: Item
instance of: scholarly article
title: Class number one criteria for real quadratic fields. II
zbMATH Open document ID: 0625.12003
author: Richard A. Mollin
published in: Proceedings of the Japan Academy. Series A
publication date: 1987-01-01T00:00:00Z
review text: In the previous paper (see the preceding review), the author considered real quadratic fields \({\mathbb{Q}}(\sqrt{n})\) with \(n\equiv 1\) (mod 4) under a certain assumption, and gave criteria for these real quadratic fields to have class number one. In this paper, he deals with positive square-free integers n of R-D type, and intends to generalize results by \textit{T. Azuhara} [Nagoya Math. J. 95, 123-135 (1984; Zbl 0533.12008)], \textit{R. Sasaki} [to appear in Nagoya Math. J., Zbl 0612.12003] and himself [J. Number Theory 24, 7-19 (1986; Zbl 0591.12006)]. Namely, he gives a necessary condition for real quadratic fields \({\mathbb{Q}}(\sqrt{n})\) such that \(n=m^ 2+r>7\), 4m\(\equiv 0\) (mod r), \(-m<r\leq m\) and \(m\not\equiv 1\) (mod 4) to have class number one.
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11R29
zbMATH DE Number: 4014842
zbMATH Keywords: Richaud-Degert type
zbMATH Keywords: real quadratic fields
zbMATH Keywords: class number one
reviewed by: Hideo Yokoi
MaRDI profile type: Publication
full work available at URL: pjaa.63.162
OpenAlex ID: W4248965308
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cites work: Class number one criteria for real quadratic fields. I
cites work: Q5804241
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DOI: 10.3792/PJAA.63.162
description: scientific article; zbMATH DE number 4014842