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

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Authors	KUČERA Radan
Year of publication	2001
Type	Article in Periodical
Magazine / Source	Nagoya Mathematical Journal
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	Relative class number; imaginary abelian field
Description	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.
Related projects:	Mathematical structures of algebra and geometry