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

Publicacions Matemàtiques (1994)

- Volume: 38, Issue: 1, page 175-185
- ISSN: 0214-1493

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topVelani, 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 -

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