Abstract
The purpose of this paper is to establish an inequality connecting the lattice point enumerator of a 0-symmetric convex body with its successive minima. To this end, we introduce an optimization problem whose solution refines former methods, thus producing a better upper bound. In particular, we show that an analogue of Minkowski’s second theorem on successive minima with the volume replaced by lattice point enumerator is true up to an exponential factor, whose base is approximately 1.64.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Malikiosis, R. An Optimization Problem Related to Minkowski’s Successive Minima. Discrete Comput Geom 43, 784–797 (2010). https://doi.org/10.1007/s00454-009-9155-5
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DOI: https://doi.org/10.1007/s00454-009-9155-5