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The main result of this paper is an inequality relating the lattice pointenumerator of a 3-dimensional, 0-symmetric convex body and its successiveminima. This is an example of generalization of Minkowski's theorems onsuccessive minima, where the volume is replaced by the discrete analogue, thelattice point enumerator. This problem is still open in higher dimensions,however, we introduce a stronger conjecture that shows a possibility of proofby induction on the dimension.

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