Fundamental units in a family of cubic fields
Journal de Théorie des Nombres de Bordeaux, Volume 16 (2004) no. 3, pp. 569-575.

Let 𝒪 be the maximal order of the cubic field generated by a zero ε of x 3 +(-1)x 2 -x-1 for , 3. We prove that ε,ε-1 is a fundamental pair of units for 𝒪, if [𝒪:[ε]]/3.

Soit 𝒪 l’ordre maximal du corps cubique engendré par une racine ε de l’equation x 3 +(-1)x 2 -x-1=0, où , 3. Nous prouvons que ε,ε-1 forment un système fondamental d’unités dans 𝒪, si [𝒪:[ε]]/3.

Published online:
DOI: 10.5802/jtnb.461
Veikko Ennola 1

1 Department of Mathematics University of Turku FIN-20014, Finland
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Veikko Ennola. Fundamental units in a family of cubic fields. Journal de Théorie des Nombres de Bordeaux, Volume 16 (2004) no. 3, pp. 569-575. doi : 10.5802/jtnb.461. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.461/

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