CM fields with a reciprocal unit-primitive element

Cornelius Greither; Toufik Zaïmi

doi:10.1016/j.crma.2017.11.014

Number theory

CM fields with a reciprocal unit-primitive element

Presented by: Jean-Pierre Serre

Cornelius Greither ¹; Toufik Zaïmi ²

¹ Fakultät für Informatik, Institut für theoretische Informatik und Mathematik, Universität der Bundeswehr München, 85577 Neubiberg, Germany
² Department of Mathematics and Statistics, College of Science, Al Imam Mohammad Ibn Saud Islamic University, Riyadh 11623, Saudi Arabia

Comptes Rendus. Mathématique, Volume 356 (2018) no. 1, pp. 8-12

Abstract (Original language)
Résumé

Let K be a noncyclotomic CM field. We show that the field $K \cap R$ has a reciprocal unit-primitive element when K does. Also, we prove some related conditions that make the converse of this assertion true.

Soit K un corps CM non cyclotomique. On montre que, si K admet une unité réciproque primitive, il en est de même pour le corps $K \cap R$ . On prouve également des conditions qui rendent vraie l'inverse de cette proposition.

Received: 2017-08-11
Accepted: 2017-11-21
Published online: 2017-12-06

DOI: 10.1016/j.crma.2017.11.014

Author's affiliations:

Cornelius Greither ¹; Toufik Zaïmi ²

¹ Fakultät für Informatik, Institut für theoretische Informatik und Mathematik, Universität der Bundeswehr München, 85577 Neubiberg, Germany
² Department of Mathematics and Statistics, College of Science, Al Imam Mohammad Ibn Saud Islamic University, Riyadh 11623, Saudi Arabia

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Cornelius Greither; Toufik Zaïmi. CM fields with a reciprocal unit-primitive element. Comptes Rendus. Mathématique, Volume 356 (2018) no. 1, pp. 8-12. doi: 10.1016/j.crma.2017.11.014

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