  We investigate the Ehrhart polynomial for the class of 0-symmetric convex
lattice polytopes in Euclidean $n$-space $\mathbb{R}^n$. It turns out that the
roots of the Ehrhart polynomial and Minkowski's successive minima are closely
related by their geometric and arithmetic mean. We also show that the roots of
lattice $n$-polytopes with or without interior lattice points differ
essentially. Furthermore, we study the structure of the roots in the planar
case. Here it turns out that their distribution reflects basic properties of
lattice polygons.
