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Générateurs de l'anneau des entiers d'une extension cyclotomique

Ranieri, Gabriele. (2008) Générateurs de l'anneau des entiers d'une extension cyclotomique. Journal of Number Theory, 128 (6). pp. 1576-1586.

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Abstract

Let $p$ be an odd prime and $q = p^m$, where $m$ is a positive integer. Let $zeta_q$ be a $q$th primitive root of $1$ and $mathcal{O}_q$ be the ring of integers of $mathbb{Q}(zeta_q)$. I. Ga'al and L. Robertson showed that if $(h_q^+, p(p-1)/2) = 1$, where $h_q^+$ is the class number of $mathbb{Q}(zeta_q + overline{zeta_q})$, then if $alpha in mathcal{O}_q$ is a generator of $mathcal{O}_q$ either $alpha$ is equal to a conjugate of an integer translate of $zeta_q$ or $alpha + overline{alpha}$ is an odd integer. In this paper we show that we can remove the hypothesis over $h_q^+$. In other words we prove that if $alpha$ is a generator of $mathcal{O}_q$, then either $alpha$ is a conjugate of an integer translate of $zeta_q$ or $alpha + overline{alpha}$ is an odd integer.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik
UniBasel Contributors:Ranieri, Gabriele
Item Type:Article, refereed
Article Subtype:Research Article
Bibsysno:Link to catalogue
Publisher:Elsevier
ISSN:0022-314X
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:14 Nov 2017 14:36
Deposited On:22 Mar 2012 13:57

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