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2001 Formulae for the relative class number of an imaginary abelian field in the form of a determinant
Radan Kučera
Nagoya Math. J. 163: 167-191 (2001).

Abstract

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.

Citation

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Radan Kučera. "Formulae for the relative class number of an imaginary abelian field in the form of a determinant." Nagoya Math. J. 163 167 - 191, 2001.

Information

Published: 2001
First available in Project Euclid: 27 April 2005

zbMATH: 1002.11079
MathSciNet: MR1855194

Subjects:
Primary: 11R29
Secondary: 11R20

Rights: Copyright © 2001 Editorial Board, Nagoya Mathematical Journal

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Vol.163 • 2001
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