Omega Estimate for the Lattice Point Discrepancy of a Body of Revolution Using The Resonance Method

Abstract

Using a recent method developed by Mahatab, we obtain an improved $\Omega$-bound for the error term arising in lattice counting problem of bodies of revolution in ${\mathbb{R}}^3$ around a coordinate axis and having smooth boundary with bounded nonzero curvature. This strengthens an earlier result by Kühleitner and Nowak.

7 pages