Fundamental units in a family of cubic fields

Veikko Ennola

doi:10.5802/jtnb.461

Veikko Ennola ¹

¹ Department of Mathematics University of Turku FIN-20014, Finland

Journal de théorie des nombres de Bordeaux, Tome 16 (2004) no. 3, pp. 569-575.

Abstract (VO)
Résumé

Let $𝒪$ be the maximal order of the cubic field generated by a zero $ε$ of $x^{3} + (ℓ - 1) x^{2} - ℓ x - 1$ for $ℓ \in ℤ$ , $ℓ \geq 3$ . We prove that $ε, ε - 1$ is a fundamental pair of units for $𝒪$ , if $[𝒪 : ℤ [ε]] \leq ℓ / 3 .$

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

MR Zbl

DOI : 10.5802/jtnb.461

Affiliations des auteurs :

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, Tome 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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Cité par 8 documents. Sources : Crossref, zbMATH