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Periodic Jacobi-Perron expansions associated with a unit

Brigitte Adam;  Georges Rhin — 2011

Journal de Théorie des Nombres de Bordeaux

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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