Note on the class numbers of certain real quadratic fields
type: Item
instance of: scholarly article
title: Note on the class numbers of certain real quadratic fields
zbMATH Open document ID: 1050.11090
DOI: 10.1007/BF02941283
author: D. Massart
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 2004-05-18T00:00:00Z
review text: Let \(n\) and \(a\) be integers, \(n\geq 2\), \(a\geq 3\), \(a\) odd, and \(K_{a,n}= \mathbb{Q}(\sqrt{a^{2n}+ 4})\). Then \(\alpha= {1\over 2}(a^n+ 2+ \sqrt{a^{2n}+ 4})\) is an integer of \(K_{a,n}\) and there exists an ideal \({\mathfrak A}\) of \(K_{a,n}\) such that \((\alpha)= {\mathfrak A}^n\). The author proves that the order of the ideal class \([{\mathfrak A}]\) equals \(n\) and as a consequence of this statement he presents the main result of this paper that the class number of \(K_{a,n}\) is divisible by \(n\).
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11R29
zbMATH DE Number: 2063950
zbMATH Keywords: real quadratic field
zbMATH Keywords: class number
reviewed by: Ladislav Skula
MaRDI profile type: Publication
cites work: Some results on the Mordell-Weil group of the Jacobian of the Fermat curve
cites work: A note on quadratic fields in which a fixed prime number splits completely
cites work: A note on quadratic fields in which a fixed prime number splits completetly. III
cites work: Real quadratic fields with class numbers divisible by \(n\)
full work available at URL: https://doi.org/10.1007/bf02941283
OpenAlex ID: W2087636326
description: scientific article; zbMATH DE number 2063950