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Special values of hypergeometric functions and periods of CM elliptic curves


Author: Yifan Yang
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 11F12; Secondary 11G15, 11G18, 33C05
DOI: https://doi.org/10.1090/tran/7134
Published electronically: December 28, 2017
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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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Additional Information

Yifan Yang
Affiliation: Department of Mathematics, National Taiwan University and National Center for Theoretical Sciences, Taipei, Taiwan 106
Email: yangyifan@ntu.edu.tw

DOI: https://doi.org/10.1090/tran/7134
Received by editor(s): December 15, 2015
Received by editor(s) in revised form: November 23, 2016
Published electronically: December 28, 2017
Additional Notes: The author was partially supported by Grant 106-2115-M-002-009-MY3 of the Ministry of Science and Technology, Taiwan (R.O.C.).
Article copyright: © Copyright 2017 American Mathematical Society

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