by Henk, Martin.

**Series:** 2001-10, Preprints

- MSC:
- 52C17 Packing and covering in $n$ dimensions
- 11H31 Lattice packing and covering

**Abstract:**

The main purpose of this note is to prove an upper

bound on the number of lattice points of a centrally symmetric

convex body in terms of the successive minima of the body. This bound

improves on former bounds and narrows the gap towards a lattice

point

analogue of Minkowski's second theorem on successive minima.

Moreover, we present Minkowski's original proof of

his second theorem on successive minima. It turns out that

using the modern mathematical language

his proof is extremely elegant and short,

although it was criticized as lengthy and obscure.

**Keywords:**

successive minima, convex bodies, lattices, lattice points