by Henk, M., Wills, J. M..
Series: 2007-24, Preprints
In 1921 Blichfeldt gave an upper bound on the number of integral points contained in a convex body in terms of the volume of the body. More precisely, he showed that #$(K\cap\Z^n)\leqn! vol(K)+n,$ whenever $K\subset \R^n$ is a convex body containing $n+1$ affinely independent integral points. Here we prove an analogous inequality with respect to the surface area $F(K)$, namely #$(K\cap\Z^n)
Lattice polytopes, volume, surface area