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

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, t...

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Main Author:	Malikiosis, Romanos-Diogenes
Other Authors:	School of Physical and Mathematical Sciences
Format:	Article
Language:	English
Published:	2013
Subjects:	DRNTU::Science::Mathematics
Online Access:	https://hdl.handle.net/10356/98234 http://hdl.handle.net/10220/12320
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Institution:	Nanyang Technological University
Language:	English

id	sg-ntu-dr.10356-98234
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spelling	sg-ntu-dr.10356-982342023-02-28T19:41:10Z A discrete analogue for Minkowski’s second theorem on successive minima Malikiosis, Romanos-Diogenes School of Physical and Mathematical Sciences DRNTU::Science::Mathematics 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. Published Version 2013-07-25T09:13:17Z 2019-12-06T19:52:21Z 2013-07-25T09:13:17Z 2019-12-06T19:52:21Z 2012 2012 Journal Article Malikiosis, R.-D. (2012). A discrete analogue for Minkowski’s second theorem on successive minima. Advances in Geometry, 0(0), 1-17. https://hdl.handle.net/10356/98234 http://hdl.handle.net/10220/12320 10.1515/advgeom-2012-0002 en 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. application/pdf
institution	Nanyang Technological University
building	NTU Library
continent	Asia
country	Singapore Singapore
content_provider	NTU Library
collection	DR-NTU
language	English
topic	DRNTU::Science::Mathematics
spellingShingle	DRNTU::Science::Mathematics Malikiosis, Romanos-Diogenes A discrete analogue for Minkowski’s second theorem on successive minima
description	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.
author2	School of Physical and Mathematical Sciences
author_facet	School of Physical and Mathematical Sciences Malikiosis, Romanos-Diogenes
format	Article
author	Malikiosis, Romanos-Diogenes
author_sort	Malikiosis, Romanos-Diogenes
title	A discrete analogue for Minkowski’s second theorem on successive minima
title_short	A discrete analogue for Minkowski’s second theorem on successive minima
title_full	A discrete analogue for Minkowski’s second theorem on successive minima
title_fullStr	A discrete analogue for Minkowski’s second theorem on successive minima
title_full_unstemmed	A discrete analogue for Minkowski’s second theorem on successive minima
title_sort	discrete analogue for minkowski’s second theorem on successive minima
publishDate	2013
url	https://hdl.handle.net/10356/98234 http://hdl.handle.net/10220/12320
_version_	1759853533700554752

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

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