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Etude des interruptions dans l'algorithme de Jacobi–Perron

Published online by Cambridge University Press:  17 April 2009

Eugène Dubois ,
Ahmed Farhane  and
Roger Paysant-Le Roux
Eugène Dubois
Affiliation:
Laboratoire de Mathématiques Nicolas Oresme, UMR CNRS n∘ 6139, Université Caen, 14032 Caen-Cedex, France e-mail: eugene.dubois@math.unicaen.fr
Ahmed Farhane
Affiliation:
Département de Mathématiques et Informatique, Faculté des Sciences et Techniques de SETTAT, Maroc, e-mail: ahmed_farhane@yahoo.fr
Roger Paysant-Le Roux
Affiliation:
Laboratoire Nicolas ORESME, UMR CNRS n∘ 6139, Université de Caen14032 Caen-CedexFrance e-mail: Roger.Paysant-Lerous@math.unicaen.fr
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It is well known that in general the Jacobi–Perron algorithm (a multi-dimensional analogue of the continued fraction algorithm) may or might not acknowledge the dependence over ℚ of its arguments 1, α1,…, αn by truncating itself down to fewer arguments from some step onwards (if so, the algorithm is said to display an ‘interruption’). We show here that if n = 2 then 1, α1, α2 are linearly dependent over ℚ of and only if the Jacobi–Perron Algorithm displays an interruption. We give examples showing this is not so for any n ≥ 3.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 241 - 254
Copyright
Copyright © Australian Mathematical Society 2004

References

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