Scattering at Zero Energy for Attractive Homogeneous Potentials

We compute up to a compact term the zero-energy scattering matrix for a class of potentials asymptotically behaving as −γ|x|^−μ with 0 < μ < 2 and γ > 0. It turns out to be the propagator for the wave equation on the sphere at time . The research of J.D. is supported in part by the grant N N201 270135. Part of the research was done during a visit of both authors to the Erwin Schr?dinger Institute. Submitted: November 28, 2008. Accepted: March 2, 2009.