  Let B denote a three-dimensional body of rotation, with respect to one
coordinate axis, whose boundary is sufficiently smooth and of bounded nonzero
Gaussian curvature throughout, except for the two boundary points on the axis
of rotation, where the curvature may vanish. For a large real variable t, we
are interested in the number A(t) of integer points in the linearly dilated
body tB, in particular in the lattice discrepancy P(t) = A(t) - volume(tB). We
are able to evaluate the contribution of the boundary points of curvature zero
to P(t), with a remainder that is fairly small in mean-square.
