Successive Minima and Lattice Points
度量几何
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0204158,
title = {Successive Minima and Lattice Points},
author = {Martin Henk},
journal= {arXiv preprint arXiv:math/0204158},
year = {2007}
}