1. bookVolume 16 (2021): Edition 2 (December 2021)
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eISSN
2309-5377
Première parution
30 Dec 2013
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access type Accès libre

Divisibility Parameters and the Degree of Kummer Extensions of Number Fields

Publié en ligne: 02 Feb 2022
Volume & Edition: Volume 16 (2021) - Edition 2 (December 2021)
Pages: 71 - 88
Reçu: 13 Oct 2020
Accepté: 30 Aug 2021
Détails du magazine
License
Format
Magazine
eISSN
2309-5377
Première parution
30 Dec 2013
Périodicité
2 fois par an
Langues
Anglais
Abstract

Let K be a number field, and let be a prime number. Fix some elements α1,...r of K× which generate a subgroup of K× of rank r. Let n1,...,nr, m be positive integers with mni for every i. We show that there exist computable parametric formulas (involving only a finite case distinction) to express the degree of the Kummer extension K(ζm, α1n1,,αrnr \root {{\ell ^{{n_1}}}} \of {{\alpha _1}} , \ldots ,\root {{\ell ^{{n_r}}}} \of {{\alpha _r}} ) over K(ζm) for all n1,..., nr, m. This is achieved with a new method with respect to a previous work, namely we determine explicit formulas for the divisibility parameters which come into play.

Keywords

MSC 2010

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