Families of Thue Inequalities with Transitive Automorphisms
| dc.contributor.author | An, Wenyong | |
| dc.date.accessioned | 2014-06-17T17:15:22Z | |
| dc.date.available | 2014-06-17T17:15:22Z | |
| dc.date.issued | 2014-06-17 | |
| dc.date.submitted | 2014 | |
| dc.description.abstract | A family of parameterized Thue equations is defined as F_{t,s,...}(X, Y ) = m, m ∈ Z where F_{t,s,...}(X,Y) is a form in X and Y with degree greater than or equal to 3 and integer coefficients that are parameterized by t, s, . . . ∈ Z. A variety of these families have been studied by different authors. In this thesis, we study the following families of Thue inequalities |sx3 −tx2y−(t+3s)xy2 −sy3|≤2t+3s, |sx4 −tx3y−6sx2y2 +txy3 +sy4|≤6t+7s, |sx6 − 2tx5y − (5t + 15s)x4y2 − 20sx3y3 + 5tx2y4 +(2t + 6s)xy5 + sy6| ≤ 120t + 323s, where s and t are integers. The forms in question are “simple”, in the sense that the roots of the underlying polynomials can be permuted transitively by automorphisms. With this nice property and the hypergeometric functions, we construct sequences of good approximations to the roots of the underlying polynomials. We can then prove that under certain conditions on s and t there are upper bounds for the number of integer solutions to the above Thue inequalities. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/8530 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | Parameterized Diophantine equation | en |
| dc.subject | Thue equation and inequality | en |
| dc.subject | hypergeometric method | en |
| dc.subject.program | Pure Mathematics | en |
| dc.title | Families of Thue Inequalities with Transitive Automorphisms | en |
| dc.type | Doctoral Thesis | en |
| uws-etd.degree | Doctor of Philosophy | en |
| uws-etd.degree.department | Pure Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |