A discrete analogue for Minkowski's second theorem on successive minima

Details A discrete analogue for Minkowski's second theorem on successive minima A discrete analogue for Minkowski's second theorem on successive minima

2010-01-21

arxiv.org/abs/1001.3729v1

Mathematics

Number Theory

19 pages

Scientific paper

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.

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