Description
Let $X$ be a compact hyperbolic surface with finite order singularities and $X_1$ its unit tangent bundle. We consider the twisted Selberg zeta function $Z(s;\rho)$ associated with a representation $\rho \colon \pi_1(X_1) \to \mathrm{GL}(V_\rho)$.
In this talk, we will present recent results concerning a relation between the twisted Selberg zeta function $Z(s;\rho)$ and the regularized determinant of the twisted Laplacian. The main tool we use is the Selberg trace formula. If $X$ has no finite order singularities, we obtain as a corollary a corresponding relation. This is joint work with Jay Jorgenson and Lejla Smajlović.