Semiclassical evidence for the BGS-conjecture

Recently, M. Sieber and K. Richter achieved a breakthrough towards a proof of the BGS-conjecture by calculating semiclassically a first correction to the diagonal approximation of the orthogonal form factor for geodesic flow on a Riemann surface of constant negative curvature. In this note, we try to generalize the arguments. However, the solution proposed is not yet correct, because also other geometries must be taken into account.