Periodic representations for cubic irrationalities
Number Theory
2013-04-11 v1
Abstract
In this paper we present some results related to the problem of finding periodic representations for algebraic numbers. In particular, we analyze the problem for cubic irrationalities. We show an interesting relationship between the convergents of bifurcating continued fractions related to a couple of cubic irrationalities, and a particular generalization of the Redei polynomials. Moreover, we give a method to construct a periodic bifurcating continued fraction for any cubic root paired with another determined cubic root.
Cite
@article{arxiv.1304.2906,
title = {Periodic representations for cubic irrationalities},
author = {Marco Abrate and Stefano Barbero and Umberto Cerruti and Nadir Murru},
journal= {arXiv preprint arXiv:1304.2906},
year = {2013}
}