English

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

R2 v1 2026-06-21T20:59:09.885Z