The Shimura-Taniyama Conjecture and Conformal Field Theory
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 of Geometry and Physics
Digital Object Identifier (DOI)
Schimmrigk R and Underwood S. 2003. The shimura-taniyama conjecture and conformal field theory. J Geom Phys 48(2-3):169-89.