Fundamental units for orders of unit rank 1 and generated by a unit

Abstract : Let ε be an algebraic unit for which the rank of the group of units of the order ℤ[ε] is equal to 1. Assume that ε is not a complex root of unity. It is natural to wonder whether ε is a fundamental unit of this order. It turns out that the answer is in general yes, and that a fundamental unit of this order can be explicitly given (as an explicit polynomial in ε) in the rare cases when the answer is no. This paper is a self-contained exposition of the solution to this problem, solution which was up to now scattered in many papers in the literature.
Type de document :
Article dans une revue
Banach Center Publications, Institute of Mathematics Polish Academy of Sciences, 2016, 108, pp.173 - 189. <10.4064/bc108-0-14>
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01288083
Contributeur : Aigle I2m <>
Soumis le : lundi 14 mars 2016 - 15:42:08
Dernière modification le : lundi 4 septembre 2017 - 12:14:14

Identifiants

Collections

Citation

Stéphane R. Louboutin. Fundamental units for orders of unit rank 1 and generated by a unit. Banach Center Publications, Institute of Mathematics Polish Academy of Sciences, 2016, 108, pp.173 - 189. <10.4064/bc108-0-14>. <hal-01288083>

Partager

Métriques

Consultations de la notice

78