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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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Official URL: http://edoc.unibas.ch/dok/A5262033

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Abstract

Let p be an odd prime and q=pm, where m is a positive integer. Let zetaq be a qth primitive root of 1 and mathcalOq be the ring of integers of mathbbQ(zetaq). I. Ga'al and L. Robertson showed that if (h+q,p(p1)/2)=1, where h+q is the class number of mathbbQ(zetaq+overlinezetaq), then if alphainmathcalOq is a generator of mathcalOq either alpha is equal to a conjugate of an integer translate of zetaq or alpha+overlinealpha 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 mathcalOq, then either alpha is a conjugate of an integer translate of zetaq or alpha+overlinealpha 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
Publisher:Elsevier
ISSN:0022-314X
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
edoc DOI:
Last Modified:14 Nov 2017 14:36
Deposited On:22 Mar 2012 13:57

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