Covering lattice points by subspaces
arXiv:math/0102030 · doi:10.1023/A:1015233631926
Abstract
We find tight estimates for the minimum number of proper subspaces needed to cover all lattice points in an n-dimensional convex body symmetric about the origin. We also find the order of magnitude of the number of (n-1)-dimensional subspaces induced by the lattice points in a large n-dimensional ball centered at the origin.
10 pages, AMS-TeX; to appear in Period. Math. Hung.; Corollary to Theorem 3 has been replaced by a weaker version, because the original proof of the Corollary was incorrect. A new proof is provided and Remark 3 has been added