The $a$-points of the Selberg zeta-function are uniformly distributed modulo one

Abstract

Let $Z(s)$ be the Selberg zeta-function associated with a compact Riemann surface. We prove that the imaginary parts of the nontrivial $a$-points of $Z(s)$ are uniformly distributed modulo one. We also consider the question whether the eigenvalues of the corresponding Laplacian are uniformly distributed modulo one.