Periodic Jacobi-Perron expansions associated with a unit
Journal de Théorie des Nombres de Bordeaux, Tome 23 (2011) no. 3, pp. 527-539.

Nous démontrons que, pour toute unité ϵ dans un corps de nombres réel K de degré n+1, il existe seulement un nombre fini de n-uples dans K n qui ont un développement purement périodique par l’algorithme de Jacobi-Perron. Ce résultat généralise le cas des fractions continues pour n=1. Pour n=2 nous donnons un algorithme qui permet de calculer explicitement tous ces couples.

We prove that, for any unit ϵ in a real number field K of degree n+1, there exits only a finite number of n-tuples in K n which have a purely periodic expansion by the Jacobi-Perron algorithm. This generalizes the case of continued fractions for n=1. For n=2 we give an explicit algorithm to compute all these pairs.

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DOI : https://doi.org/10.5802/jtnb.776
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Brigitte Adam; Georges  Rhin. Periodic Jacobi-Perron expansions associated with a unit. Journal de Théorie des Nombres de Bordeaux, Tome 23 (2011) no. 3, pp. 527-539. doi : 10.5802/jtnb.776. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.776/

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