Relationship between the discrete and resonance spectrum for the Laplace operator on a noncompact hyperbolic Riemann surface (Q2291262)

The article under review establishes a refinement of the Selberg trace formula for a cofinite and non-cocompact subgroup \(\Gamma\) of \(\operatorname{PSL}(2,\mathbb R)\) that relates the discrete spectrum of the Laplace operator on \(\Gamma\backslash H^2\) with the poles of the scattering matrix (i.e., the resonance spectrum). As an application, the author observed in [Izv. Math. 83, No. 5, 1066--1079 (2019; Zbl 1489.11079); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 83, No. 5, 167--180 (2019)] that (from the last page) ``the distribution of primes can be reconstructed from the discrete spectrum of the Laplace operator for \(\Gamma = \operatorname{SL}(2,\mathbb Z)\)''.