Ein Gitterpunktproblem in der hyperbolischen Ebene

  • Tobias Martin

    Hochschule für Technik, Wirtschaft und Kultur, Leipzig, Germany

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 tt \to \infty of the function A(t,z,z)A (t, z, z’) giving the number of zz’-equivalent points in the circle around zz with radius tt 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)A (t, z, z’) and the iterated lattice point function.

Cite this article

Tobias Martin, Ein Gitterpunktproblem in der hyperbolischen Ebene. Z. Anal. Anwend. 8 (1989), no. 2, pp. 103–120

DOI 10.4171/ZAA/341