Successive Minima and Lattice Points
Abstract
Description
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.
Minkowski's proof of his second theorem is rather lengthy and it was
also criticised as obscure. We present a short proof of Minkowski's
second theorem on successive minima, which, however, is based on the
ideas of Minkowski's proof.