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dc.creatorRothlisberger, Mark Peter
dc.date.accessioned2010-12-14T15:26:02Z
dc.date.accessioned2010-12-14T15:26:07Z
dc.date.available2010-12-14T15:26:02Z
dc.date.available2010-12-14T15:26:07Z
dc.date.created2010-08
dc.date.issued2010-12-14
dc.date.submittedAugust 2010
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2010-08-1834
dc.descriptiontext
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.
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.subjectNumber field
dc.subjectKorkin-Zolotarev
dc.subjectBasis reduction
dc.titleAn analogue of the Korkin-Zolotarev lattice reduction for vector spaces over number fields
dc.date.updated2010-12-14T15:26:07Z
dc.description.departmentMathematics
dc.type.genrethesis*
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Texas at Austin
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy


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