Best simultaneous diophantine approximations of some cubic algebraic numbers
Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 403-414.

Soit α un nombre algébrique réel de degré 3 dont les conjugués ne sont pas réels. Il existe une unité ζ de l’anneau des entiers de K=ℚ(α) pour laquelle il est possible de décrire l’ensemble de tous les vecteurs meilleurs approximations de θ=(ζ,ζ 2 ).

Let α be a real algebraic number of degree 3 over ℚ whose conjugates are not real. There exists an unit ζ of the ring of integer of K=ℚ(α) for which it is possible to describe the set of all best approximation vectors of θ=(ζ,ζ 2 ).’

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Chevallier, Nicolas. Best simultaneous diophantine approximations of some cubic algebraic numbers. Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 403-414. http://archive.numdam.org/item/JTNB_2002__14_2_403_0/

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