On zeros of the derivative of the three-dimensional Selberg zeta function

Abstract

In this article, we study the distribution of zeros of the derivative of the Selberg zeta function for compact three-dimensional hyperbolic spaces. We obtain an asymptotic formula for the counting function of its zeros. This is a three-dimensional version of the celebrated work of Wenzhi Luo. We also deduce other asymptotic formulas relating to its zeros from the above formula.