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=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(p−1)/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 |
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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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