The trace formula for a point scatterer on a compact hyperbolic surface

Abstract: An exact trace formula for the perturbation of the Laplacian by a Dirac delta potential on a compact hyperbolic Riemann surface is derived. The formula can be considered an analogue of the Selberg trace formula. The difference of perturbed and unperturbed trace is expressed as an identity term plus a sum over combinations of diffractive orbits which visit the position of the potential.