Class numbers of cubic cyclic fields
type: Item
instance of: scholarly article
title: Class numbers of cubic cyclic fields
zbMATH Open document ID: 0281.12007
published in: Journal of the Mathematical Society of Japan
publication date: 1974-01-01T00:00:00Z
review text: Let \(n\) be any given positive integer. It is known that there exist real (imaginary) quadratic fields whose class numbers are divisible by \(n\). This is classical for the imaginary case and the real case was proved by \textit{Y. Yamamoto} [ Osaka J. Math. 7, 57--76 (1970; Zbl 0222.12003)]. It is shown in this paper that the same is true for cubic cyclic fields. We deal with fields defined by equations \(X^3+pX^2+2pX+p=0\) for integers \(p\) and special properties of these equations play essential roles.
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R16
Mathematics Subject Classification ID: 11R20
zbMATH DE Number: 3440521
author: Koji Uchida
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/02630447
OpenAlex ID: W2002823933
DOI: 10.2969/JMSJ/02630447
description: scientific article; zbMATH DE number 3440521