  The leading (Gaussian) fluctuation correction to the weak coupling zero
temperature BCS superconducting gap equation is computed. We find that the
dominant contribution comes from the high energies and momenta (compared to the
gap) and gives a correction smaller by the weak-coupling factor $gN_0$ than the
mean-field terms. This correction is small due to cancellation of singular
contributions from the amplitude and phase mode at high energies and momenta.
