no. 1
Number theory
CM fields with a reciprocal unit-primitive element
[Corps CM ayant une unité reciproque primitive]

Présenté par : Jean-Pierre Serre

Greither, Cornelius1 ; Zaïmi, Toufik2
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, Tome 356 (2018) no. 1, pp. 8-12.

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∩R. On prouve également des conditions qui rendent vraie l'inverse de cette proposition.

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

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.11.014
Greither, Cornelius 1 ; Zaïmi, Toufik 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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Greither, Cornelius; Zaïmi, Toufik. CM fields with a reciprocal unit-primitive element. Comptes Rendus. Mathématique, Tome 356 (2018) no. 1, pp. 8-12. doi : 10.1016/j.crma.2017.11.014. http://www.numdam.org/articles/10.1016/j.crma.2017.11.014/

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