A discrete analogue for Minkowski%26apos;s second theorem on successive minima

作者：Malikiosis Romanos Diogenes^*

来源：Advances in Geometry, 2012, 12(2): 365-380.

DOI：10.1515/advgeom-2012-0002

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%26apos;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.

• 出版日期2012-3
• 单位南阳理工学院