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Formulae for the relative class number of an imaginary abelian field in the form of a determinant
- Source :
- Nagoya Math. J. 163 (2001), 167-191
- Publication Year :
- 2001
- Publisher :
- Cambridge University Press (CUP), 2001.
-
Abstract
- 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.
- Subjects :
- Discrete mathematics
010308 nuclear & particles physics
General Mathematics
010102 general mathematics
Zero (complex analysis)
11R29
Field (mathematics)
Imaginary number
01 natural sciences
0103 physical sciences
Ideal (ring theory)
0101 mathematics
Abelian group
Class number
The Imaginary
11R20
Arithmetic of abelian varieties
Mathematics
Subjects
Details
- ISSN :
- 21526842 and 00277630
- Volume :
- 163
- Database :
- OpenAIRE
- Journal :
- Nagoya Mathematical Journal
- Accession number :
- edsair.doi.dedup.....936d31b3bcfb1cc7fd05da62dc305626