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For an arbitrary cocompact hyperbolic Coxeter group G with finite generator set S and complete growth function f S (x) = P (x)/Q(x) , we provide a recursion formula for the coefficients of the denominator polynomial Q(x). It allows to determine recursively the Taylor coefficients and to study the arithmetic nature of the poles of the growth function f S (x)… (More)

- Ruth Kellerhals
- 2009

We provide an explicit thick and thin decomposition for oriented hyperbolic manifolds M of dimension 5. The result implies improved universal lower bounds for the volume vol 5 (M) and, for M compact, new estimates relating the injectivity radius and the diameter of M with vol 5 (M). The quantification of the thin part is based upon the identification of the… (More)

By different scissors congruence techniques a number of dissection identities are presented between certain quasi-Coxeter polytopes, whose parameters are related to the golden section, and an ideal regular simplex in hyperbolic 5-space. As a consequence, several hyperbolic polyhedral 5-volumes can be computed explicitly in terms of Apéry's constant ζ(3) and… (More)

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