Beiträge zur Algebra und Geometrie <BR> Contributions to Algebra and GeometryVol. 40, No. 2, pp. 351-361 (1999)

Galleries in Poincare Half-spaces and Diophantine Approximation

Pierrick Meignen

Structures Discretes et Analyse Diophantienne, U.F.R. des Sciences, Universite de Caen, Esplanade de la Paix, 14032 Caen, France, e-mail:

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

Full text of the article:

[Previous Article] [Next Article] [Contents of this Number]