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 of the function giving the number of -equivalent points in the circle around with radius 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 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. 103–120DOI 10.4171/ZAA/341