I will present recent progress on the evaluation of one-loop string amplitudes at finite energies. I will explain a general technique inspired from analytic number theory that evaluates these amplitudes in terms of an infinite series originating from certain Lorentzian singularities in moduli space. I will mostly focus on the concrete example of the one-loop four-graviton scattering amplitude for type II superstrings and the physics we can extract from these methods, especially its behavior in the high-energy limit. This talk is based on joint works with M.M. Baccianti, J. Chandra, T. Hartman and S. Mizera.