Article contents
A lattice-point problem in hyperbolic space
Published online by Cambridge University Press: 26 February 2010
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
- Information
- Copyright
- Copyright © University College London 1975
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), 357–386.Google Scholar
2. Huber, H.. “ Über eine neue Klasse automorpher Funktionen und ein Gitterpunktproblem in der hyperbolischen Ebene ”, Comm. Math. Helv., 30 (1956), 20–62.Google Scholar
3. Huber, H.. “ Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen ”, I, Math. Ann. 138 (1959), 1–26; II Math. Ann., 142 (1961), 385–398 and 143 (1961), 463–464.Google Scholar
5. Neunhüffer, H.. Über die analytische Forsetzung von Poincaré-Reihen, Dissertation (Heidelberg).Google Scholar
7. Roecke, W., “ Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene ”. I, Math. Ann., 167 (1966), 292–337; 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), 47–87.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
- 47
- Cited by