no. 3
Fundamental units in a family of cubic fields
Ennola, Veikko1
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.

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

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

DOI : 10.5802/jtnb.461
Ennola, Veikko 1

1 Department of Mathematics University of Turku FIN-20014, Finland 
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Ennola, Veikko. 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. http://www.numdam.org/articles/10.5802/jtnb.461/

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