Formulae for the relative class number of an imaginary abelian field in the form of a product of determinants
| Authors | |
|---|---|
| Year of publication | 2002 |
| Type | Article in Periodical |
| Magazine / Source | Acta Mathematica et Informatica Universitatis Ostraviensis |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | Relative class number |
| Description | 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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