Ein Gitterpunktproblem in der hyperbolischen Ebene

Abstract

A lattice point problem in hyperbolic plane on which acts a Fuchsian group of the first kind is considered. In this connection the asymptotic behaviour at $t\to \infty$ of the function $A(t,z,z’)$ giving the number of $z’$-equivalent points in the circle around $z$ with radius $t$ is investigated. Besides the main terms there is given an estimation of the remaining part improving previous results. As a most important instrument there serves the mean value method based on a functional equation between $A(t,z,z’)$ and the iterated lattice point function.