The Selberg Zeta-Function of a Kleinian Group
作者： S.J. PATTERSON
DOI: 10.1016/B978-0-12-067570-8.50031-7
关键词:
摘要: Publisher Summary This chapter focuses on the Selberg zeta-function of a Kleinian group. The trace formula was introduced for cocompact discrete groups as an infinite analog Kronecker class-number formula. It describes relationship between geometric and spectral properties such showed how it possible, in certain cases, to extend cases where group acts symmetric space rank 1 has quotient finite volume, but not necessarily cocompact. He also could be reformulated analytic function, zeta-function. made use special Fuchsian does higher dimensional cases. class convex acting hyperbolic spaces arbitrary dimension.
sci-hub.se 参考文章(14)
J. Elstrodt, F. Grunewald, J. Mennicke, The Selberg zeta-function for cocompact discrete subgroups of PSL(2,C) Banach Center Publications. ,vol. 17, pp. 83- 120 ,(1985) , 10.4064/-17-1-83-120
Henrik Schlichtkrull, Hyperfunctions and Harmonic Analysis on Symmetric Spaces ,(1984)
Laurent Guillope, Sur la distribution des longueurs des geodesiques fermees d’une surface compacte a bord totalement geodesique Duke Mathematical Journal. ,vol. 53, pp. 827- 848 ,(1986) , 10.1215/S0012-7094-86-05345-7
David Fried, The zeta functions of Ruelle and Selberg. I Annales Scientifiques De L Ecole Normale Superieure. ,vol. 19, pp. 491- 517 ,(1986) , 10.24033/ASENS.1515
William P. Thurston, The geometry and topology of 3-manifolds [Massachusetts Institute of Technology, Dept. of Mathematics]. ,(1979)
Rafe R Mazzeo, Richard B Melrose, Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature Journal of Functional Analysis. ,vol. 75, pp. 260- 310 ,(1987) , 10.1016/0022-1236(87)90097-8
Pierre-Yves Gaillard, Transformation de Poisson de formes differentielles. Le cas de l’espace hyperbolique Commentarii Mathematici Helvetici. ,vol. 61, pp. 581- 616 ,(1986) , 10.1007/BF02621934
S. J. Patterson, On a lattice-point problem in hyperbolic space and related questions in spectral theory Arkiv för Matematik. ,vol. 26, pp. 167- 172 ,(1988) , 10.1007/BF02386116
S. J. Patterson, Spectral theory and Fuchsian groups Mathematical Proceedings of the Cambridge Philosophical Society. ,vol. 81, pp. 59- 75 ,(1977) , 10.1017/S030500410000027X
David Ruelle, Zeta-functions for expanding maps and Anosov flows Inventiones Mathematicae. ,vol. 34, pp. 231- 242 ,(1976) , 10.1007/BF01403069