Generating functions for the numbers of Abelian extensions of a local field
The aim of this paper is to give an explicit formula for the num- bers of abelian extensions of a p-adic number field and to study the generating function of these numbers. More precisely, we give the number of abelian ex- tensions with given degree and ramification index, and the number of abelian...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 1990 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/7664 |
| Acceso en línea: | https://hdl.handle.net/2445/7664 |
| Access Level: | acceso abierto |
| Palabra clave: | Teoria de cossos de classe Teoria algebraica de nombres Class field theory Algebraic number theory |
| Sumario: | The aim of this paper is to give an explicit formula for the num- bers of abelian extensions of a p-adic number field and to study the generating function of these numbers. More precisely, we give the number of abelian ex- tensions with given degree and ramification index, and the number of abelian extensions with given degree of any local field of characteristic zero. Moreover, we give a concrete expression of a generating function for these last numbers |
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