An application of metric diophantine approximation in hyperbolic space to quadratic forms.

Título inglés An application of metric diophantine approximation in hyperbolic space to quadratic forms.
Título español Una aplicación de la aproximación diofántica métrica en el espacio hiperbólico a las formas cuadráticas.
Autor/es Velani, Sanju L.
Organización Dep. Math. Univ. York, Heslington, Reino Unido
Revista 0214-1493
Publicación 1994, 38 (1): 175-185, 14 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés For any real τ, a lim sup set WG,y(τ) of τ-(well)-approximable points is defined for discrete groups G acting on the Poincaré model of hyperbolic space. Here y is a 'distinguished point' on the sphere at infinity whose orbit under G corresponds to the rationals (which can be regarded as the orbit of the point at infinity under the modular group) in the classical theory of diophantine approximation.
In this paper the Hausdorff dimension of the set WG,y(τ) is determined for geometrically finite groups of the first kind. Consequently, by considering the hyperboloid model of hyperbolic space, this result is shown to have a natural but non trivial interpretation in terms of quadratic forms.
Clasificación UNESCO 120503
Palabras clave español Formas cuadráticas ; Problemas diofánticos ; Espacio hiperbólico
Código MathReviews MR1291959
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