Successive Minima and Lattice Points

By Martin Henk. 2002

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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.

Subfields: Applied Mathematics, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/eac5a0f1f8cf6f4ee514e42606f0b49bc8a0eac4