@article{7b3ef0503da040339d4bbfd13915f842,
title = "The growth rates of ideal coxeter polyhedra in hyperbolic 3-space",
abstract = "In [7], Kellerhals and Perren conjectured that the growth rates of the reflection groups given by compact hyperbolic Coxeter polyhedra are always Perron numbers. We prove that this conjecture holds in the context of ideal Coxeter polyhedra in H3. Our methods allow us to bound from below the growth rates of composite ideal Coxeter polyhedra by the growth rates of its ideal Coxeter polyhedral constituents.",
keywords = "Cusp, Growth rate, Hyperbolic Coxeter polyhedron, Perron number",
author = "Jun Nonaka and Ruth Kellerhals",
note = "Funding Information: ACKNOWLEDGMENT. The first author would like to show his greatest appreciation to Professor Hiroyasu Izeki who provided valuable comments and suggestions. He would also like to thank Dr. Alexander Kolpakov for valuable comments. The second author was partially supported by Schweizerischer Nationalfonds 200020–156104. The authors would also like to thank the referee for helpful comments.",
year = "2017",
month = dec,
doi = "10.3836/tjm/1502179234",
language = "English",
volume = "40",
pages = "379--391",
journal = "Tokyo Journal of Mathematics",
issn = "0387-3870",
publisher = "Publication Committee for the Tokyo Journal of Mathematics",
number = "2",
}