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dc.contributor.authorPyott, Nolan
dc.date.accessioned2023-08-31 15:47:01 (GMT)
dc.date.available2023-08-31 15:47:01 (GMT)
dc.date.issued2023-08-31
dc.date.submitted2027-08-24
dc.identifier.urihttp://hdl.handle.net/10012/19818
dc.description.abstractStarting with an analysis of the result that for any coprime integers a and b, and some ϵ > 0, we have eventually that gcd(a^n − 1,b^n − 1) < a^ϵn holds for all n, we are motivated to look for geometric reasons why this should hold. After some discussion on the general geometry and arithmetic needed to examine these questions, we take a quick look into how Vojta’s conjectures provide a generalization of our first result. In particular, we also note a case where this implies a similar equality on particular elliptic curves.en
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectdiophantine geometryen
dc.subjectVojta's conjectureen
dc.subjectalgebraic geometryen
dc.subjectarithmeticen
dc.subjectgcden
dc.subjectelliptic curveen
dc.subjectprojective varietyen
dc.titleGeneralized GCDs as Applications of Vojta’s Conjectureen
dc.typeMaster Thesisen
dc.pendingfalse
uws-etd.degree.departmentPure Mathematicsen
uws-etd.degree.disciplinePure Mathematicsen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws-etd.embargo.terms0en
uws.contributor.advisorMcKinnon, David
uws.contributor.affiliation1Faculty of Mathematicsen
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


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