Jay Jorgenson: On the distribution of zeros of the derivative of the Selberg zeta function

Associated to any Fuchsian group of the first kind, there is a zeta function defined by Selberg whose Euler product encodes the length spectrum on the associated Riemann surface and whose divisor encodes the spectral theory of the hyperbolic Laplacian. In joint work with Lejla Smajlovic, we studied the divisor of the derivative of the Selberg zeta function, and we obtained asymptotic results regarding the vertical and horizontal distribution of the divisor of the derivative. Specific examples are explored, namely the setting of congruence subgroups and "moonshine" groups.