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Main Title: Interpolating between volume and lattice point enumerator with successive minima
Author(s): Freyer, Ansgar
Lucas, Eduardo
Other Contributor(s): Nature, Springer
Type: Article
Abstract: We study inequalities that simultaneously relate the number of lattice points, the volume and the successive minima of a convex body to one another. One main ingredient in order to establish these relations is Blaschke’s shaking procedure, by which the problem can be reduced from arbitrary convex bodies to anti-blocking bodies. As a consequence of our results, we obtain an upper bound on the lattice point enumerator in terms of the successive minima, which is equivalent to Minkowski’s upper bound on the volume in terms of the successive minima.
Subject(s): lattice points in convex bodies
successive minima
Minkowski’s second theorem
Blaschke’s shaking procedure
Issue Date: 11-May-2022
Date Available: 18-Jul-2022
Language Code: en
DDC Class: 510 Mathematik
Sponsor/Funder: TU Berlin, Open-Access-Mittel – 2022
Journal Title: Monatshefte für Mathematik
Publisher: Springer Nature
Volume: 198
Publisher DOI: 10.1007/s00605-022-01713-1
Page Start: 717
Page End: 740
EISSN: 1436-5081
ISSN: 0026-9255
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik » FG Diskrete Mathematik / Geometrie
Appears in Collections:Technische Universität Berlin » Publications

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