Arithmetic distributions of convergents arising from Jacobi-Perron algorithm

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.

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

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

2000 AMS Subject Classification: Primary 11K50

Metric and Arithmetic Properties of Mediant-rosen Maps

We define maps which induce mediant convergents of Rosen continued fractions and discuss arithmetic and metric properties of mediant convergents. In particular, we show equality of the ergodic theoretic Lenstra constant with the arithmetic Legendre constant for each of these maps. This value is sufficiently small that the mediant Rosen convergents directly determine the Hurwitz constant of Diop...