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Isaac Newton Institute for Mathematical Sciences

Scattering on a decorated star-graph as a toy model for the spectral theory of automorphic functions

15th February 2007

Author: Geyler, V (Mordovian State)


A compact Riemannian manifold of dimension less than 4 with a finite number of semi-lines attached to the manifold is considered. It is shown that there is a deep analogy between the scattering and spectral properties of Schrodinger operators for this hybrid manifold and those for the automorphic Laplacian on Riemann surfaces with cusps. As an application, a relation between the scattering amplitude for hybrid manifolds with underlying compact Riemann surfaces of constant negative curvature and the Selberg zeta-function for this surface is obtained.