Salem numbers, spectral radii and growth rates of hyperbolic Coxeter groups
Group Theory
2025-12-15 v2 Geometric Topology
Number Theory
Abstract
We show that not every Salem number appears as the growth rate of a cocompact hyperbolic Coxeter group. We also give a new proof of the fact that the growth rates of planar hyperbolic Coxeter groups are spectral radii of Coxeter transformations, and show that this need not be the case for growth rates of hyperbolic tetrahedral Coxeter groups.
Keywords
Cite
@article{arxiv.2008.10965,
title = {Salem numbers, spectral radii and growth rates of hyperbolic Coxeter groups},
author = {Ruth Kellerhals and Livio Liechti},
journal= {arXiv preprint arXiv:2008.10965},
year = {2025}
}
Comments
24 pages, 3 figures