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Formulae for the relative class number of an imaginary abelian field in the form of a determinant

Published online by Cambridge University Press:  22 January 2016

Radan Kučera
Radan Kučera*
Affiliation:
Department of Mathematics, Faculty of Science, Masaryk University, Janáčkovo nám. 2a, 662 95 Brno, Czech Republic, kucera@math.muni.cz
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Abstract

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There is in the literature a lot of determinant formulae involving the relative class number of an imaginary abelian field. Usually such a formula contains a factor which is equal to zero for many fields and so it gives no information about the class number of these fields. The aim of this paper is to show a way of obtaining most of these formulae in a unique fashion, namely by means of the Stickelberger ideal. Moreover some new and non-vanishing formulae are derived by a modification of Ramachandra’s construction of independent cyclotomic units.

Keywords

11R2911R20
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 163 , September 2001 , pp. 167 - 191
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

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