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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Detalles Bibliográficos
Autor: Travesa i Grau, Artur
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
Descripción
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