  For a convex body B in three-dimensional Euclidean space, which is invariant
under rotations around one coordinate axis and has a smooth boundary of bounded
nonzero curvature, the lattice point discrepancy (number of integer points
minus volume) of a linearly enlarged copy of B is estimated from below. On the
basis of a recent method of K. Soundararajan, an Omega-bound is obtained that
improves upon all earlier results of this kind.
