On periodic sequences for algebraic numbers
Number Theory
2007-05-23 v3
Abstract
For each positive integer n greater than or equal to 2, a new approach to expressing real numbers as sequences of nonnegative integers is given. The n=2 case is equivalent to the standard continued fraction algorithm. For n=3, it reduces to a new iteration of the triangle. Cubic irrationals that are roots of x^3 + k x^2 + x - 1 are shown to be precisely those numbers with purely periodic expansions of period length one. For general positive integers n, it reduces to a new iteration of an n dimensional simplex.
Cite
@article{arxiv.math/9906016,
title = {On periodic sequences for algebraic numbers},
author = {Thomas Garrity},
journal= {arXiv preprint arXiv:math/9906016},
year = {2007}
}
Comments
22 pages. An error in section five of the original paper has been corrected, resulting in some slight alterations in the statements in the theorems in section six