On volumes of hyperbolic Coxeter polytopes and quadratic forms

John G. Ratcliffe; Steven T. Tschantz

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arXiv · 1203.6648

On volumes of hyperbolic Coxeter polytopes and quadratic forms

John G. Ratcliffe·Steven T. Tschantz

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Abstract

In this paper, we compute the covolume of the group of units of the quadratic form f_d^n(x) = x_1^2 + x_2^2 + . . . + x_n^2 - d x_{n+1}^2 with d an odd, positive, square-free integer. Mcleod has determined the hyperbolic Coxeter fundamental domain of the reflection subgroup of the group of units of the quadratic form f_3^n. We apply our covolume formula to compute the volumes of these hyperbolic Coxeter polytopes.

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John G. Ratcliffe, Steven T. Tschantz. 2012-03-29. On volumes of hyperbolic Coxeter polytopes and quadratic forms. https://arxiv.org/abs/1203.6648

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