Galleries in Poincare Half-spaces and Diophantine Approximation

Abstract: \font\msbm=msbm10 \def\bbR{\hbox{\msbm R}} In this paper, we present a multidimensional generalization of a geometrical method of approximation devised by G. Humbert. Introducing Clifford algebras and hyperbolic reflection groups with unbounded fundamental domains of finite volume, we obtain a complete set of results which are traditionally connected with the modular group and the usual continued fraction expansions in $\bbR$.

Keywords: Hyperbolic reflection groups, Diophantine approximation

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