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

Warning

This publication doesn't include Institute of Computer Science. It includes Faculty of Science. Official publication website can be found on muni.cz.

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