By Steven Zelditch
This paintings is anxious with a couple of twin asymptotics difficulties on a finite-area hyperbolic floor. the 1st challenge is to figure out the distribution of closed geodesics within the unit tangent package. The author's effects provide a quantitative shape to Bowen's equidistribution thought: they refine Bowen's theorem a lot because the top geodesic theorem on hyperbolic quotients refines the asymptotic formulation for the variety of closed geodesics of size lower than T. specifically, the writer supplies a cost of equidistribution when it comes to low eigenvalues of the Laplacian. the second one challenge is to figure out the distribution of eigenfunctions (in microlocal experience) within the unit tangent package deal. the most outcome right here (which is required for the equidistribution concept of closed geodesics) is an evidence of a signed and averaged model of the suggest Lindelof speculation for Rankin-Selberg zeta services. the most instrument used here's a generalization of Selberg's hint formulation.
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