Bounds on the density of smooth lattice coverings

Or Ordentlich, Oded Regev, Barak Weiss

Let $K$ be a convex body in ${\mathbb{R}}^n$, let $L$ be a lattice with covolume one, and let $\eta >0$. We say that $K$ and $L$ form an $\eta$-smooth cover if each point $x \in \mathbb{R}^…