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dc.contributor.advisorVaaler, Jeffrey D.en
dc.creatorRothlisberger, Mark Peteren
dc.date.accessioned2010-12-14T15:26:02Zen
dc.date.accessioned2010-12-14T15:26:07Zen
dc.date.available2010-12-14T15:26:02Zen
dc.date.available2010-12-14T15:26:07Zen
dc.date.issued2010-08en
dc.date.submittedAugust 2010en
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2010-08-1834en
dc.descriptiontexten
dc.description.abstractWe show the existence of a basis for a vector space over a number field with two key properties. First, the n-th basis vector has a small twisted height which is bounded above by a quantity involving the n-th successive minima associated with the twisted height. Second, at each place v of the number field, the images of the basis vectors under the automorphism associated with the twisted height satisfy near-orthogonality conditions analagous to those introduced by Korkin and Zolotarev in the classical Geometry of Numbers. Using this basis, we bound the Mahler product associated with the twisted height. This is the product of a successive minimum of a twisted height with the corresponding successive minimum of its dual twisted height. Previous work by Roy and Thunder in [12] showed that the Mahler product was bounded above by a quantity which grows exponentially as the dimension of the vector space increases. In this work, we demonstrate an upper bound that exhibits polynomial growth as the dimension of the vector space increases.en
dc.format.mimetypeapplication/pdfen
dc.language.isoengen
dc.subjectNumber fielden
dc.subjectKorkin-Zolotareven
dc.subjectBasis reductionen
dc.titleAn analogue of the Korkin-Zolotarev lattice reduction for vector spaces over number fieldsen
dc.date.updated2010-12-14T15:26:07Zen
dc.contributor.committeeMemberHelm, Daviden
dc.contributor.committeeMemberRodriguez-Villegas, Fernandoen
dc.contributor.committeeMemberVoloch, Felipeen
dc.contributor.committeeMemberFukshansky, Lennyen
dc.description.departmentMathematicsen
dc.type.genrethesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorUniversity of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen


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