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The Shimura-Taniyama Conjecture and Conformal Field Theory

Rolf Schimmrigk·Sean Underwood
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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.

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Rolf Schimmrigk, Sean Underwood. 2002-11-28. The Shimura-Taniyama Conjecture and Conformal Field Theory. https://doi.org/10.1016/s0393-0440(03)00030-5

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