Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Supervisors info:
Αριστείδης Κοντογεώργης , Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Άγγελος Κουτσιανάς, Επίκουρος Καθηγητής, Τμήμα Μαθηματικών, ΑΠΘ
Original Title:
Applications of the Modularity Theorem to Diophantine Equations
Translated title:
Applications of the Modularity Theorem to Diophantine Equations
Summary:
The main topic of this thesis is teh generalization of the techniques used in Wile's proof of the FLT on a broader category of Diophantine equations. The core methodology is the use of Ribet's Level Lowering Theorem in order to attach a space of newforms of level $N$ to an elliptic curve $E$ arising in some way from our Diophantine equation. The project examines first this connection between elliptic curves and newforms and then uses these techniques on specific Diophantine equations.
Main subject category:
Science
Keywords:
modularity, modular forms, newforms, elliptic curves, Diophantine equations
