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Zeitschrift für Analysis und ihre Anwendungen

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Volume 8, Issue 2, 1989, pp. 103–120
DOI: 10.4171/ZAA/341

Published online: 1989-04-30

Ein Gitterpunktproblem in der hyperbolischen Ebene

Tobias Martin[1]

(1) Hochschule für Technik, Wirtschaft und Kultur, Leipzig, Germany

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.

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Martin Tobias: Ein Gitterpunktproblem in der hyperbolischen Ebene. Z. Anal. Anwend. 8 (1989), 103-120. doi: 10.4171/ZAA/341