Polyxeni Spilioti, "Determinants of twisted Laplacians and the twisted Selberg zeta function."

mardi 17 mars 2026, 10:30 → 12:30 Europe/Paris

 

In this talk, we consider a compact hyperbolic surface with finite order singularities and its unit tangent bundle.

We consider also the twisted Selberg zeta function associated with an arbitrary, finite-dimensional representation of the fundamental group of the unit tangent bundle.

We will present recent results concerning a relation between the twisted Selberg zeta function and the regularized determinant of the twisted Laplacian. The main tool we use is the Selberg trace formula. If the surface 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.