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Currently displaying 1 – 2 of 2

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Généralisation d'une famille de Shanks

Brigitte Adam — 1998

Acta Arithmetica

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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