A two-dimensional continued fractions algorithm with Lagrange and Dirichlet properties
Number Theory
2015-02-17 v1
Abstract
A Lagrange Theorem in dimension 2 is proved, for a particular two-dimensional algorithm, with a very natural geometrical definition. Dirichlet-type properties for the convergence of the algorithm are also proved. These properties procced from a geometrical quality of the algorithm. Some refercences are given to the works of various authors, in the domain of multidimensional continued fractions algorithms.
Cite
@article{arxiv.1502.04231,
title = {A two-dimensional continued fractions algorithm with Lagrange and Dirichlet properties},
author = {Christian Drouin},
journal= {arXiv preprint arXiv:1502.04231},
year = {2015}
}
Comments
Published in the Journal de Th\'eorie des Nombres de Bordeaux