A discrete analogue for Minkowski’s second theorem on successive minima
Date of Issue2012
School of Physical and Mathematical Sciences
The main result of this paper is an inequality relating the lattice point enumerator of a 3-dimensional, 0-symmetric convex body and its successive minima. This is an example of generalization of Minkowski's theorems on successive minima, where the volume is replaced by the discrete analogue, the lattice point enumerator. This problem is still open in higher dimensions, however, we introduce a stronger conjecture that shows a possibility of proof by induction on the dimension.
Advances in geometry
© 2012 De Gruyter. This paper was published in Advances in Geometry and is made available as an electronic reprint (preprint) with permission of De Gruyter. The paper can be found at the following official DOI: [http://dx.doi.org/10.1515/advgeom-2012-0002]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.