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dc.contributor.authorGonzález Merino, Bernardo
dc.contributor.authorHenze, Matthias
dc.date.accessioned2015-03-27T12:00:00Z
dc.date.accessioned2016-10-05T14:14:00Z
dc.date.available2015-03-27T12:00:00Z
dc.date.available2016-10-05T14:14:00Z
dc.date.issued2014
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1089
dc.descriptionResearch in Pairs 2014en_US
dc.description.abstractOne of the most fruitful results from Minkowski’s geometric viewpoint on number theory is his so called 1st Fundamental Theorem. It provides an optimal upper bound for the volume of an o-symmetric convex body whose only interior lattice point is the origin. Minkowski also obtained a discrete analog by proving optimal upper bounds on the number of lattice points in the boundary of such convex bodies. Whereas the volume inequality has been generalized to any number of interior lattice points already by van der Corput in the 1930s, a corresponding result for the discrete case remained to be proven. Our main contribution is a corresponding optimal relation between the number of boundary and interior lattice points of an o-symmetric convex body. The proof relies on a congruence argument and a difference set estimate from additive combinatorics.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2014,17
dc.subjectConvex bodyen_US
dc.subjectLattice pointen_US
dc.subjectMinkowski’s fundamental theoremen_US
dc.subjectDiscrete analogen_US
dc.subjectDifference set estimateen_US
dc.subjectSuccessive minimumen_US
dc.titleA Generalization of the Discrete Version of Minkowski’s Fundamental Theoremen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2014-17
local.scientificprogramResearch in Pairs 2014
local.series.idOWP-2014-17
local.subject.msc52
local.subject.msc11
dc.identifier.urnurn:nbn:de:101:1-2015032612455
dc.identifier.ppn1655701622


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