A remark on the class number of the maximal real subfield of a cyclotomic field. II
type: Item
instance of: scholarly article
title: A remark on the class number of the maximal real subfield of a cyclotomic field. II
zbMATH Open document ID: 0771.11043
author: Hiroyuki Osada
published in: Proceedings of the Japan Academy. Series A
publication date: 1993-01-17T00:00:00Z
review text: [Part I, cf. ibid. 65, No. 9, 318-319 (1989; Zbl 0704.11039).] In this paper, the author considers the class number \(h_ K\) of the maximal real subfield \(K\) of a cyclotomic field \(\mathbb{Q}(\zeta_ q)\) with prime \(q\) satisfying \(q=4p+1\) for a prime \(p\) and the class number \(h_ F\) of the real quadratic subfield \(\mathbb{Q}(\sqrt{q})=F\), and proves by purely algebraic method that \(h_ K=h_ F\) holds if \(h_ K<q\), \(p+1\) is not a power of 2 and \(2p+1\) is not a power of 3. For a review of Part III (see below).
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R18
zbMATH DE Number: 97925
zbMATH Keywords: class number
zbMATH Keywords: maximal real subfield
zbMATH Keywords: cyclotomic field
zbMATH Keywords: real quadratic subfield
reviewed by: Hideo Yokoi
MaRDI profile type: Publication
full work available at URL: pjaa.68.41
OpenAlex ID: W4234512290
cites work: Class Number Computations of Real Abelian Number Fields
cites work: Q3864603
cites work: Q4402415
cites work: Q5690489
DOI: 10.3792/PJAA.68.41
description: scientific article; zbMATH DE number 97925