Generalized GCDs as Applications of Vojta’s Conjecture
| dc.contributor.author | Pyott, Nolan | |
| dc.date.accessioned | 2023-08-31T15:47:01Z | |
| dc.date.available | 2023-08-31T15:47:01Z | |
| dc.date.issued | 2023-08-31 | |
| dc.date.submitted | 2027-08-24 | |
| dc.description.abstract | Starting 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.identifier.uri | http://hdl.handle.net/10012/19818 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | diophantine geometry | en |
| dc.subject | Vojta's conjecture | en |
| dc.subject | algebraic geometry | en |
| dc.subject | arithmetic | en |
| dc.subject | gcd | en |
| dc.subject | elliptic curve | en |
| dc.subject | projective variety | en |
| dc.title | Generalized GCDs as Applications of Vojta’s Conjecture | en |
| dc.type | Master Thesis | en |
| uws-etd.degree | Master of Mathematics | en |
| uws-etd.degree.department | Pure Mathematics | en |
| uws-etd.degree.discipline | Pure Mathematics | en |
| uws-etd.degree.grantor | University of Waterloo | en |
| uws-etd.embargo.terms | 0 | en |
| uws.contributor.advisor | McKinnon, David | |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.published.city | Waterloo | en |
| uws.published.country | Canada | en |
| uws.published.province | Ontario | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |