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arXiv · 1503.07971

Special values of hypergeometric functions and periods of CM elliptic curves

Yifan Yang
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Abstract

Let $X_0^6(1)/W_6$ be the Atkin-Lehner quotient of the Shimura curve $X_0^6(1)$ associated to a maximal order in an indefinite quaternion algebra of discriminant $6$ over $\mathbb Q$. By realizing modular forms on $X_0^6(1)/W_6$ in two ways, one in terms of hypergeometric functions and the other in terms of Borcherds forms, and using Schofer's formula for values of Borcherds forms at CM-points, we obtain special values of certain hypergeometric functions in terms of periods of elliptic curves over $\overline\mathbb Q$ with complex multiplication.

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Yifan Yang. 2015-03-27. Special values of hypergeometric functions and periods of CM elliptic curves. https://arxiv.org/abs/1503.07971

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