A study of the zero set of the Selberg Zeta function

It is well known (since 1956) that the Selberg Zeta function for compact surfaces satisfies the “Riemann Hypothesis”: any zero in the critical strip 0 < R(s) < 1 is either real or Im(s) = 1/2. The question of location and distribution of the zeros of the Selberg Zeta function associated to a noncompact hyperbolic surface attracted attention of the mathematics community in 2014 when numerical experiments by D. Borthwick showed sets of a rich and complex structure. We will give an overview of the computational methods used, present recent results, justifying some old observations as well as state open conjectures.