On two-dimensional continued fractions for the integer hyperbolic matrices with small norm
Number Theory
2009-11-17 v1
Abstract
In this note we classify two-dimensional continued fractions for cubic irrationalities constructed by matrices with not large norm (). The classification is based on the following new result: the class of matrices with an irreducible characteristic polynomial over the field of rational numbers is the class of matrices of frobenius type iff there exists an integer solution for a certain equation with integer coefficients.
Cite
@article{arxiv.0911.3040,
title = {On two-dimensional continued fractions for the integer hyperbolic matrices with small norm},
author = {Oleg Karpenkov},
journal= {arXiv preprint arXiv:0911.3040},
year = {2009}
}