Determinants of twisted Laplacians and the twisted Selberg zeta function

par Polyxeni Spilioti (Université de Patras)

mardi 31 mars 2026, 10:30 → 11:30 Europe/Paris

1180 (Bât. E2) (Tours)

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 $\rho : \pi_1(X_1 ) \to GL(V_\rho)$. 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. These results can be viewed as an extension to the non-unitary twists case of the results by Sarnak and Naud. This is joint work with Jay Jorgenson and Lejla Smajlovic.