A Numerical Study of Eigenvalues of the Hyperbolic Laplacian for Polyhedra with One Cusp

Huntebrinker's research was supported by the Deutsche Forschungsgemeinschaft. Let H 3 be three-dimensional hyperbolic space and a group of isometries of H 3 that acts discontinuously on H 3 and that has a fundamental domain of finite hyperbolic volume. The Laplace operator of H 3 gives rise to a positive, essentially selfadjoint operator on L2( nH 3). The nature of its discrete spectrum dspec is still not well understood if is not cocompact. This paper contains a report on a numerical study of dspec for various noncocompact groups . Particularly interesting are the results for some nonarithmetic groups .