A two-dimensional continued fraction algorithm with Lagrange and Dirichlet properties

Christian Drouin[1]

  • [1] 26 Avenue d’Yreye 40 510 SEIGNOSSE FRANCE

Journal de Théorie des Nombres de Bordeaux (2014)

  • Volume: 26, Issue: 2, page 307-346
  • ISSN: 1246-7405

Abstract

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A Lagrange Theorem in dimension 2 is proved in this paper, for a particular two dimensional continued fraction algorithm, with a very natural geometrical definition. Dirichlet type properties for the convergence of this algorithm are also proved. These properties proceed from a geometrical quality of the algorithm. The links between all these properties are studied. In relation with this algorithm, some references are given to the works of various authors, in the domain of multidimensional continued fractions algorithms.

How to cite

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Drouin, Christian. "A two-dimensional continued fraction algorithm with Lagrange and Dirichlet properties." Journal de Théorie des Nombres de Bordeaux 26.2 (2014): 307-346. <http://eudml.org/doc/275743>.

@article{Drouin2014,
abstract = {A Lagrange Theorem in dimension 2 is proved in this paper, for a particular two dimensional continued fraction algorithm, with a very natural geometrical definition. Dirichlet type properties for the convergence of this algorithm are also proved. These properties proceed from a geometrical quality of the algorithm. The links between all these properties are studied. In relation with this algorithm, some references are given to the works of various authors, in the domain of multidimensional continued fractions algorithms.},
affiliation = {26 Avenue d’Yreye 40 510 SEIGNOSSE FRANCE},
author = {Drouin, Christian},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
month = {10},
number = {2},
pages = {307-346},
publisher = {Société Arithmétique de Bordeaux},
title = {A two-dimensional continued fraction algorithm with Lagrange and Dirichlet properties},
url = {http://eudml.org/doc/275743},
volume = {26},
year = {2014},
}

TY - JOUR
AU - Drouin, Christian
TI - A two-dimensional continued fraction algorithm with Lagrange and Dirichlet properties
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2014/10//
PB - Société Arithmétique de Bordeaux
VL - 26
IS - 2
SP - 307
EP - 346
AB - A Lagrange Theorem in dimension 2 is proved in this paper, for a particular two dimensional continued fraction algorithm, with a very natural geometrical definition. Dirichlet type properties for the convergence of this algorithm are also proved. These properties proceed from a geometrical quality of the algorithm. The links between all these properties are studied. In relation with this algorithm, some references are given to the works of various authors, in the domain of multidimensional continued fractions algorithms.
LA - eng
UR - http://eudml.org/doc/275743
ER -

References

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