Comments on the height reducing property
Number Theory
2012-12-21 v2
Abstract
A complex number alpha is said to satisfy the height reducing property if there is a finite subset F of the ring Z of the rational integers such that Z[alpha]=F[alpha]. This problem of finding F has been considered by several authors, especially in contexts related to self affine tilings, and expansions of real numbers in non-integer bases. We continue, in this note, the description of the numbers satisfying the height reducing property, and we specify a related characterization of the roots of integer polynomials with dominant term.
Keywords
Cite
@article{arxiv.1205.1184,
title = {Comments on the height reducing property},
author = {Shigeki Akiyama and Toufik Zaimi},
journal= {arXiv preprint arXiv:1205.1184},
year = {2012}
}
Comments
Revised Version. To appear in Central European Journal of Mathematics