A 3-dimensional periodic Jacobi-Perron algorithm of period length 8

On the Singularization of the Two-Dimensional Jacobi-Perron Algorithm

2000 AMS Subject Classification: Primary 11K50

Periodic Jacobi-Perron expansions associated with a unit

We prove that, for any unit in a real number fieldK of degree n+ 1, there exits only a finite number of n-tuples in K 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.

The two-dimensional Jacobi-Perron Algorithm is S-equivalent to the Podsypanin Algorithm

We show that the two-dimensional Podsypanin Algorithm and the two-dimensional Jacobi-Perron Algorithm belong to the same class of Sexpansions. In particular, we show that each step of the conversion process described in Schratzberger 2007 [16], based on the techniques of Singularization and Insertion, terminates after finitely many states a.e.

Arithmetic distributions of convergents arising from Jacobi-Perron algorithm

We study the distribution modulo m of the convergents associated with the d-dimensional Jacobi-Perron algorithm for a.e. real numbers in (0, 1) by proving the ergodicity of a skew product of the Jacobi-Perron transformation; this skew product was initially introdued in [6] for regular continued fractions.

A class of transcendental numbers with explicit g - adic expansion and the Jacobi – Perron algorithm