  The QCD beta-function and the anomalous dimensions for the Coulomb potential
and the static potential first differ at three loop order. We evaluate the
three loop ultrasoft anomalous dimension for the Coulomb potential and give the
complete three loop running. Using this result, we calculate the leading
logarithmic Lamb shift for a heavy quark-antiquark bound state, which includes
all contributions to the binding energies of the form m\alpha_s^4(\alpha_s
ln\alpha_s)^k, k\ge 0.
