Generalized R\'edei rational functions and rational approximations over conics
Number Theory
2012-09-05 v1
Abstract
In this paper we study a general class of conics starting from a quotient field. We give a group structure over these conics generalizing the construction of a group over the Pell hyperbola. Furthermore, we generalize the definition of R\'edei rational functions in order to use them for evaluating powers of points over these conics. Finally, we study rational approximations of irrational numbers over conics, obtaining a new result for the approximation of quadratic irrationalities.
Cite
@article{arxiv.1209.0573,
title = {Generalized R\'edei rational functions and rational approximations over conics},
author = {Stefano Barbero and Umberto Cerruti and Nadir Murru},
journal= {arXiv preprint arXiv:1209.0573},
year = {2012}
}
Comments
11 pages