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

Velani, Sanju L.. "An application of metric diophantine approximation in hyperbolic space to quadratic forms.." Publicacions Matemàtiques 38.1 (1994): 175-185. <http://eudml.org/doc/41199>.

@article{Velani1994,
abstract = {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.},
author = {Velani, Sanju L.},
journal = {Publicacions Matemàtiques},
keywords = {Formas cuadráticas; Problemas diofánticos; Espacio hiperbólico},
language = {eng},
number = {1},
pages = {175-185},
title = {An application of metric diophantine approximation in hyperbolic space to quadratic forms.},
url = {http://eudml.org/doc/41199},
volume = {38},
year = {1994},
}

TY - JOUR
AU - Velani, Sanju L.
TI - An application of metric diophantine approximation in hyperbolic space to quadratic forms.
JO - Publicacions Matemàtiques
PY - 1994
VL - 38
IS - 1
SP - 175
EP - 185
AB - 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.
LA - eng
KW - Formas cuadráticas; Problemas diofánticos; Espacio hiperbólico
UR - http://eudml.org/doc/41199
ER -