Tables of ideal class groups of real quadratic fields
type: Item
instance of: scholarly article
title: Tables of ideal class groups of real quadratic fields
zbMATH Open document ID: 0671.12003
author: Michiyo Saito
author: Hideo Wada
published in: Proceedings of the Japan Academy. Series A
publication date: 1988-01-01T00:00:00Z
review text: The authors gave a table of the ideal class groups of imaginary quadratic fields \({\mathbb{Q}}(\sqrt{-m})\), \(m<100,000\) [(*) the authors, Sophia Kokyuroku Math. 28 (Tokyo 1988; Zbl 0629.12003)], and H. Wada gave a table of the ideal class numbers (and the sign of the norm of the principal unit) of real quadratic fields \({\mathbb{Q}}(\sqrt{m})\), \(m<100,000\) [(**) \textit{H. Wada}, Sophia Kokyuroku Math. 10 (Tokyo 1981; Zbl 0536.12001)]. By the methods of (*) the authors now give a list of the class groups (in the narrow and in the wide sense) for all these real fields of (**). By genus theory the 2-rank of these groups is known. It is astonishing that there are few class groups which are not cyclic (for \(t\leq 2)\) or of the form (as abelian group) (2a,2,...,2) (for \(t>2)\) (where t is the number of ramified primes in \({\mathbb{Q}}(\sqrt{m}))\), and therefore these tables cover only two pages.
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 65A05
zbMATH DE Number: 4097508
zbMATH Keywords: ideal class numbers
zbMATH Keywords: real quadratic fields
reviewed by: Bernd Richter
MaRDI profile type: Publication
full work available at URL: pjaa.64.347
OpenAlex ID: W2071458793
cites work: Zur Axiomatik der ganzen und der reellen Zahlen
cites work: Q4401919
cites work: Q3320485
cites work: Q3765869
DOI: 10.3792/PJAA.64.347
description: scientific article; zbMATH DE number 4097508