Interpolating between volume and lattice point enumerator with successive minima

dc.contributor.authorFreyer, Ansgar
dc.contributor.authorLucas, Eduardo
dc.contributor.otherNature, Springer
dc.date.accessioned2022-07-18T14:42:18Z
dc.date.available2022-07-18T14:42:18Z
dc.date.issued2022-05-11
dc.description.abstractWe 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.sponsorshipTU Berlin, Open-Access-Mittel – 2022en
dc.identifier.eissn1436-5081
dc.identifier.issn0026-9255
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/17198
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-15977
dc.language.isoenen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subject.ddc510 Mathematikde
dc.subject.otherlattice points in convex bodiesen
dc.subject.othersuccessive minimaen
dc.subject.otherMinkowski’s second theoremen
dc.subject.otherBlaschke’s shaking procedureen
dc.titleInterpolating between volume and lattice point enumerator with successive minimaen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.doi10.1007/s00605-022-01713-1en
dcterms.bibliographicCitation.journaltitleMonatshefte für Mathematiken
dcterms.bibliographicCitation.originalpublishernameSpringer Natureen
dcterms.bibliographicCitation.originalpublisherplaceHeidelbergen
dcterms.bibliographicCitation.pageend740en
dcterms.bibliographicCitation.pagestart717en
dcterms.bibliographicCitation.volume198en
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Diskrete Mathematik / Geometriede
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Diskrete Mathematik / Geometriede
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
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