The Congruent Number Problem and Tunnell's Theorem

Specialeforsvar ved Bryan William Advocaat

Titel: The Congruent Number Problem and Tunnell’s Theorem

 Abstract: this thesis we provide a proof of Tunnell’s Theorem, which links the congruent number problem to the Fourier coefficients of specific half-integer weight modular forms. We start by providing a proof of the Mordell-Weil Theorem. After that, we give the definitions and required properties of modular forms of both integer weight and half-integer weight, and we state a theorem by Shimura which links these. In the fourth chapter, we mention the L-functions of both elliptic curves and modular forms and their relation. The final chapter combines all the knowledge from the previous chapters to obtain the proof of Tunnell’s Theorem.

Vejleder: Ian Kiming
Censor: Tom Høholdt, DTU