On class numbers of quadratic extensions of algebraic number fields
type: Item
instance of: scholarly article
title: On class numbers of quadratic extensions of algebraic number fields
zbMATH Open document ID: 0659.12009
published in: Proceedings of the Japan Academy. Series A
publication date: 1986-01-01T00:00:00Z
review text: Let \(t>1\) be any integer. It is proved that for any algebraic number field having a totally ramified rational odd prime p there are infinitely many quadratic extensions L of K such that \(t| h(L)\). Furthermore, L may be chosen to be of the form K(\(\sqrt{n})\) where n is any square-free rational integer of the form \(r^ 2-m^ 2\) so that p does not divide n and r is restricted by the equation \(r^ 2\leq m^{t-1}(m-1)\).
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11R11
zbMATH DE Number: 4077382
zbMATH Keywords: class number
zbMATH Keywords: quadratic extensions
author: Richard A. Mollin
MaRDI profile type: Publication
full work available at URL: pjaa.62.33
OpenAlex ID: W2086940231
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DOI: 10.3792/PJAA.62.33
description: scientific article; zbMATH DE number 4077382