An analogue of the Korkin-Zolotarev lattice reduction for vector spaces over number fields

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An analogue of the Korkin-Zolotarev lattice reduction for vector spaces over number fields

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dc.contributor.advisor Vaaler, Jeffrey D.
dc.creator Rothlisberger, Mark Peter
dc.date.accessioned 2010-12-14T15:26:02Z
dc.date.accessioned 2010-12-14T15:26:07Z
dc.date.available 2010-12-14T15:26:02Z
dc.date.available 2010-12-14T15:26:07Z
dc.date.created 2010-08
dc.date.issued 2010-12-14
dc.date.submitted August 2010
dc.identifier.uri http://hdl.handle.net/2152/ETD-UT-2010-08-1834
dc.description.abstract We 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.mimetype application/pdf
dc.language.iso eng
dc.subject Number field
dc.subject Korkin-Zolotarev
dc.subject Basis reduction
dc.title An analogue of the Korkin-Zolotarev lattice reduction for vector spaces over number fields
dc.date.updated 2010-12-14T15:26:07Z
dc.contributor.committeeMember Helm, David
dc.contributor.committeeMember Rodriguez-Villegas, Fernando
dc.contributor.committeeMember Voloch, Felipe
dc.contributor.committeeMember Fukshansky, Lenny
dc.description.department Mathematics
dc.type.genre thesis
dc.type.material text
thesis.degree.department Mathematics
thesis.degree.discipline Mathematics
thesis.degree.grantor University of Texas at Austin
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy

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