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

TL;DR

This paper improves the lower bound on the error term in counting lattice points inside bodies of revolution in three-dimensional space, using the resonance method, thereby strengthening previous results.

Contribution

It introduces an enhanced Omega estimate for the lattice point discrepancy of bodies of revolution utilizing Mahatab's resonance method, advancing prior bounds.

Findings

Established a stronger Omega bound for the lattice discrepancy

Applied the resonance method to bodies of revolution in 3D

Improved upon previous results by Kühleitner and Nowak

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 K\"uhleitner and Nowak.