Interpolating between volume and lattice point enumerator with successive minima
| dc.contributor.author | Freyer, Ansgar | |
| dc.contributor.author | Lucas, Eduardo | |
| dc.date.accessioned | 2022-07-18T14:42:18Z | |
| dc.date.available | 2022-07-18T14:42:18Z | |
| dc.date.issued | 2022-05-11 | |
| dc.description.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. | en |
| dc.description.sponsorship | TU Berlin, Open-Access-Mittel – 2022 | en |
| dc.identifier.eissn | 1436-5081 | |
| dc.identifier.issn | 0026-9255 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/17198 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-15977 | |
| dc.language.iso | en | en |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en |
| dc.subject.ddc | 510 Mathematik | de |
| dc.subject.other | lattice points in convex bodies | en |
| dc.subject.other | successive minima | en |
| dc.subject.other | Minkowski’s second theorem | en |
| dc.subject.other | Blaschke’s shaking procedure | en |
| dc.title | Interpolating between volume and lattice point enumerator with successive minima | en |
| dc.type | Article | en |
| dc.type.version | publishedVersion | en |
| dcterms.bibliographicCitation.doi | 10.1007/s00605-022-01713-1 | en |
| dcterms.bibliographicCitation.journaltitle | Monatshefte für Mathematik | en |
| dcterms.bibliographicCitation.originalpublishername | Springer Nature | en |
| dcterms.bibliographicCitation.originalpublisherplace | Heidelberg | en |
| dcterms.bibliographicCitation.pageend | 740 | en |
| dcterms.bibliographicCitation.pagestart | 717 | en |
| dcterms.bibliographicCitation.volume | 198 | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Diskrete Mathematik / Geometrie | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.group | FG Diskrete Mathematik / Geometrie | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |