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A lattice-point problem in hyperbolic space

Published online by Cambridge University Press:  26 February 2010

S. J. Patterson
Affiliation:
Mathematisches Institut der Universität, 34 Güttingen, Bunsenstr, 3/5.
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Extract

In this paper we shall discuss the following problem. Let G be a Fuchsian group of the first kind acting on the upper half-plane H. For z1, z2 ∈ H we set

Type
Research Article
Copyright
Copyright © University College London 1975

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References

1. Fadeev, L. D.. “ Expansion in eigenfunctions of the Laplace operator on the fundamental domain of a discrete group on the Lobačevskil plane ”, Trans. Moscow Math. Soc, 17 (1967), 357386.Google Scholar
2. Huber, H.. “ Über eine neue Klasse automorpher Funktionen und ein Gitterpunktproblem in der hyperbolischen Ebene ”, Comm. Math. Helv., 30 (1956), 2062.Google Scholar
3. Huber, H.. “ Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen ”, I, Math. Ann. 138 (1959), 126; II Math. Ann., 142 (1961), 385–398 and 143 (1961), 463–464.Google Scholar
4. Kubota, T.. Elementary theory of Eisenstein series. (Kodansha Ltd., Tokyo, (1973).Google Scholar
5. Neunhüffer, H.. Über die analytische Forsetzung von Poincaré-Reihen, Dissertation (Heidelberg).Google Scholar
6. Patterson, S. J..“ The limit set of a Fuchsian group, II ”, to appear.Google Scholar
7. Roecke, W., “ Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene ”. I, Math. Ann., 167 (1966), 292337; II, Math. Ann., 168 (1967), 261–324.CrossRefGoogle Scholar
8. Selberg, A.. “ Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series ”, J. Indian Math. Soc, 20 (1956), 4787.Google Scholar
9. Selberg, A.. “ Discontinuous groups and harmonic analysis ”, Proc. I.C.M. Stockholm, (1962).Google Scholar
10. Selberg, A.. “ On the estimation of Fourier coefficients of modular forms ”, Proc. Symp. Pure Math. VIII. (AMS, (1965).CrossRefGoogle Scholar
11. Whittaker, E. T. and Watson, G. N.. Modern Analysis (Cambridge, (1946).Google Scholar