On lattice points in large convex bodies

Abstract

We consider a compact convex body $\mathcal{B}$ in $\mathbb{R}^d$ $(d\geqslant 3)$ with smooth boundary and nonzero Gaussian curvature and prove a new estimate of $P_{\mathcal{B}}(t)$, the remainder in the lattice point problem, which improves previously known best result.