Growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers

Abstract

In this paper we consider the growth rates of 3-dimensional hyperbolic Coxeter polyhedra some of its dihedral angles are $\frac{\pi }{m}$ for $m\ge 7$. By combining with the classical result by Parry \cite{Pa} and the main result of \cite{Y}, we prove that the growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1603.04592; text overlap with arXiv:1504.06718 by other authors