We study the set G of growth rates of ideal Coxeter groups in hyperbolic 3-space; this set consists of real algebraic integers greater than 1. We show that (1) G is unbounded above while it has the minimum, (2) any element of G is a Perron number, and (3) growth rates of ideal Coxeter groups with n generators are located in the closed interval [n - 3, n - 1].
|ジャーナル||Proceedings of the Japan Academy Series A: Mathematical Sciences|
|出版ステータス||Published - 2015|
ASJC Scopus subject areas
- 数学 (全般)