The University of Arizona: Zelditch’s trace formula and effective Bowen’s theorem

In 1989, Zelditch considered the trace of an invariant operator composed with a pseudo-differential operator. The resulting trace formula turned out to be extremely useful in studying the distribution of closed geodesics on hyperbolic surfaces. I will demonstrate the simplest case of the proof, and discuss how things can be generalized to higher dimensional hyperbolic manifolds. This is a joint work with Insung Park.