Publication details
Formulae for the relative class number of an imaginary abelian field in the form of a determinant
| Authors | |
|---|---|
| Year of publication | 2001 |
| Type | Article in Periodical |
| Magazine / Source | Nagoya Mathematical Journal |
| MU Faculty or unit | |
| 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. |
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