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

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KUČERA Radan

Rok publikování 2002
Druh Článek v odborném periodiku
Časopis / Zdroj Acta Mathematica et Informatica Universitatis Ostraviensis
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
Obor Obecná matematika
Klíčová slova Relative class number
Popis There is in the literature a lot of deteminant formulae involving the relative class number of an imaginary abelian number field. Most of these formulae can be obtained in a unique way by means of the Stickelberger ideal. Some papers giving the relative class number formula for intermediate fields of the cyclotomic Zp-extension of an imaginary abelian field in the form of a product of determinants have appeared recently. The aim of this note is to show that it is not essential to assume that we deal with a layer in the cyclotomic Zp-extension, the similar construction can be done for any extension of abelian fields.
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