On an analogue of Selberg's eigenvalue conjecture for
Sultan Catto, Jonathan Huntley, Jay Jorgenson and David Tepper
Proc. Amer. Math. Soc. 126 (1998), 3455-3459
Primary 11F55; Secondary 22E40, 11F72
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Abstract: Let be the homogeneous space associated to the group
. Let where and consider the first nontrivial eigenvalue of the Laplacian on . Using geometric considerations, we prove the inequality . Since the continuous spectrum is represented by the band , our bound on can be viewed as an analogue of Selberg's eigenvalue conjecture for quotients of the hyperbolic half space.
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The Graduate School and Baruch College, The City University of New York, New York, New York 10010 and Department of Physics, The Rockefeller University, 1230 York Avenue, New York, New York 10021-6339
Department of Mathematics, Baruch College CUNY, 17 Lexington Avenue, New York, New York 10010
School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
Address at time of publication:
Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Received by editor(s):
January 28, 1997
The first named author acknowledges support from DOE grants DE-AC-0276-ER3074 and 3075 and PSC-CUNY Research Award No. 9203393.
The second named author acknowledges support from several PSC-CUNY grants. The third named author acknowledges support from NSF grant DMS-93-07023 and from the Sloan Foundation.
Dennis A. Hejhal
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