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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Generating functions for the numbers of abelian extensions of a local field
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by Artur Travesa PDF
Proc. Amer. Math. Soc. 108 (1990), 331-339 Request permission

Abstract:

The aim of this paper is to give an explicit formula for the numbers of abelian extensions of a ${\mathbf {p}}$-adic number field and to study the generating function of these numbers. More precisely, we give the number of abelian extensions 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.
References
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    • A. Travesa, Nombres d’extensions abelianes i les seves funcions generatrius, Doctoral Thesis, Universitat de Barcelona, 1987. —, Sobre el número de extensiones de grado dado de un cuerpo local, Actas de las X Jornadas Hispano-Lusas de Matemáticas, Sección I: Álgebra y Fundamentos, Murcia, 1985, pp. 235-243.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 108 (1990), 331-339
  • MSC: Primary 11S15; Secondary 11S40
  • DOI: https://doi.org/10.1090/S0002-9939-1990-1007513-6
  • MathSciNet review: 1007513