Nomden, Stef (2025) Asymptotic integral solu- tions to Aa^p + Bb^p = Cc^3 over number fields. Master's Thesis / Essay, Mathematics.
|
Text
mMATH2025NomdenS.pdf Download (887kB) | Preview |
|
![[img]](https://fse.studenttheses.ub.rug.nl/style/images/fileicons/text.png) |
Text
Toestemming.pdf Restricted to Registered users only Download (116kB) |
Abstract
In this thesis we apply the modular method to show the non-existence of certain asymptotic solutions to the equation Aa^p +Bb^p = Cc^3 over the ring of integers of a number field K. The modular method uses the conjectured relation between modular forms and elliptic curves. To introduce these ideas we cover the necessary details of elliptic curves and Galois theory. The latter is studied, in great detail, using Galois representations. Finally, we specialize our number field K to imaginary quadratic extensions of Q. This specialization requires a close study of S-units and S-unit equations over these fields.
| Item Type: | Thesis (Master's Thesis / Essay) |
|---|---|
| Supervisor name: | Ozman, E. and Kilicer, P. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 02 Jul 2025 10:29 |
| Last Modified: | 02 Jul 2025 10:29 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/35763 |
Actions (login required)
 |
View Item |