Resultants and height bounds for zeros of homogeneous polynomial systems

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dc.contributor.advisorVaaler, Jeffrey D.
dc.creatorRauh, Nikolas Marcelen
dc.date.accessioned2013-07-26T19:53:48Zen
dc.date.accessioned2017-05-11T22:33:22Z
dc.date.available2017-05-11T22:33:22Z
dc.date.issued2013-05en
dc.date.submittedMay 2013en
dc.date.updated2013-07-26T19:53:49Zen
dc.descriptiontexten
dc.description.abstractIn 1955, Cassels proved a now celebrated theorem giving a search bound algorithm for determining whether a quadratic form has a nontrivial zero over the rationals. Since then, his work has been greatly generalized, but most of these newer techniques do not follow his original method of proof. In this thesis, we revisit his 1955 proof, modernize his tools and language, and use this machinery to prove more general theorems regarding height bounds for the common zeros of a system of polynomials in terms of the heights of those polynomials. We then use these theorems to give a short proof of a more general (albeit, known) version of Cassels' Theorem and give some weaker results concerning the rational points of a cubic or a pair of quadratics.en
dc.description.departmentMathematicsen
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/2152/20950en
dc.language.isoen_USen
dc.subjectHomogeneous polynomialen
dc.subjectResultanten
dc.subjectHeight functionen
dc.subjectArithmetic Bezouten
dc.subjectCassels search bounden
dc.subjectQuadratic formen
dc.subjectCubic formen
dc.subjectSmall solutionen
dc.titleResultants and height bounds for zeros of homogeneous polynomial systemsen

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