Isogenous tori and the class number formulae
type: Item
instance of: scholarly article
title: Isogenous tori and the class number formulae
zbMATH Open document ID: 0774.11065
author: Shin-ichi Katayama
published in: Journal of Mathematics of Kyoto University
publication date: 1992-09-27T00:00:00Z
review text: First, the author gives the detailed proofs of the results announced in his previous papers [Proc. Japan Acad., Ser. A 62, 216--218 (1986; Zbl 0613.12004), ibid. 62, 320--322 (1986; Zbl 0613.12005)], in which he generalized the result of \textit{T. Ono} [Nagoya Math. J. 107, 121--133 (1987; Zbl 0642.12018)]. Next, he generalizes the Dirichlet class number relation for bicyclic biquadratic extension \(K/F\), using purely algebraic methods. As a corollary of this formula, he obtains the well known class number formula for \(\mathbb Q(\sqrt q,\sqrt {-1})\), where \(q\) is prime.
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R16
Mathematics Subject Classification ID: 14M25
zbMATH DE Number: 59736
zbMATH Keywords: class number of algebraic tori
zbMATH Keywords: Dirichlet class number relation
zbMATH Keywords: bicyclic biquadratic extension
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519723
OpenAlex ID: W1542695185
DOI: 10.1215/KJM/1250519723
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description: scientific article; zbMATH DE number 59736