Construction of certain real quadratic fields
type: Item
instance of: scholarly article
title: Construction of certain real quadratic fields
zbMATH Open document ID: 0538.12001
author: Tsuyoshi Uehara
published in: Proceedings of the Japan Academy. Series A
publication date: 1983-01-01T00:00:00Z
review text: In this paper, the author proves the following theorem: For an arbitrarily given natural number n and a square-free rational integer \(k>1\) satisfying some conditions, \(\epsilon =(kn^ 2\pm 2+n\sqrt{m})/2\) with \(m=k(kn^ 2\pm 4)\) is the fundamental unit of the real quadratic field \({\mathbb{Q}}(\sqrt{m})\). This is a partial generalization of the reviewer's former result, which gives the fundamental unit of \({\mathbb{Q}}(\sqrt{m})\) in the same form [J. Number Theory 2, 106-115 (1970; Zbl 0201.057)]. By means of valuation, he also gives another proof of the well-known theorem that there exist infinitely many real quadratic fields with the class number divisible by an arbitrarily given natural number n.
reviewed by: Hideo Yokoi
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 11R23
zbMATH DE Number: 3855237
zbMATH Keywords: fundamental unit
zbMATH Keywords: real quadratic field
zbMATH Keywords: class number
MaRDI profile type: Publication
full work available at URL: pjaa.59.390
OpenAlex ID: W2000157299
cites work: On units of real quadratic number fields
cites work: Q3955465
cites work: Real quadratic fields with class numbers divisible by \(n\)
cites work: On unramified Galois extensions of quadratic number fields
DOI: 10.3792/PJAA.59.390
description: scientific article; zbMATH DE number 3855237