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.  For a convex body$$\mathcal{B}$$ in$$\mathbb{R}^3 $$ which is invariant under rotations around one coordinate axis and has a smooth boundary of bounded nonzero curvature, the lattice point discrepancy$$P_\mathcal{B} (t)$$ (number of integer points minus volume) of a linearly dilated copy$$\sqrt t \mathcal{B}$$ is estimated from below. On the basis of a recent method of K. Soundararajan [16], an -bound is obtained that improves upon all earlier results of this kind.

The lattice point discrepancy of a body of revolution: Improving the lower bound by Soundararajan?s method