Zeros of the derivative of a Selberg zeta function

Abstract

In this talk, we will study the distribution of non-trivial zeros of Selberg zeta functions on cofinite hyperbolic surfaces, in particular obtain the asymptotic formula for the zero density with bounded height, which is similar to the well-known Weyl law. Then we will relate the distribution of the zeros to the issue of bounding the multiplicity of Laplacian eigenvalues.