An application of metric Diophantine approximation in hyperbolic space to Quadratic Forms

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JournalPublicacions Matematique
DatePublished - 1994
Issue number1
Volume38
Number of pages11
Pages (from-to)175-185
Original languageEnglish

Abstract

For any real T, a lim sup set WGty (T) of T-(well)-approximabl e
points is defined for discrete groups ~ acting on the Poincar é
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 diophantin e
approximation .
In this paper the Hausdorff dimension of the set WG, y (T} 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 interpretatio n
in terms of quadratic forms .

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