Title

The Shimura-Taniyama Conjecture and Conformal Field Theory

Department

Physics

Document Type

Article

Publication Date

11-2003

Abstract

The Shimura-Taniyama conjecture states that the Mellin transform of the Hasse-Weil L-function of any elliptic curve defined over the rational numbers is a modular form. Recent work of Wiles, Taylor-Wiles and Breuil-Conrad-Diamond-Taylor has provided a proof of this longstanding conjecture. Elliptic curves provide the simplest framework for a class of Calabi-Yau manifolds which have been conjectured to be exactly solvable. It is shown that the Hasse-Weil modular form determined by the arithmetic structure of the Fermat type elliptic curve is related in a natural way to a modular form arising from the character of a conformal field theory derived from an affine Kac-Moody algebra.

Journal

Journal of Geometry and Physics

Journal ISSN

0393-0440

Volume

48

Issue

2

First Page

169

Last Page

189

Digital Object Identifier (DOI)

10.1016/S0393-0440(03)00030-5