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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Algebraic transformations of hypergeometric functions and automorphic forms on Shimura curves


Authors: Fang-Ting Tu and Yifan Yang
Journal: Trans. Amer. Math. Soc. 365 (2013), 6697-6729
MSC (2010): Primary 11F12; Secondary 11G18, 33C05
Published electronically: July 26, 2013
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Abstract: In this paper, we will obtain new algebraic transformations of the $ {}_2F_1$-hypergeometric functions. The main novelty in our approach is the interpretation of identities among $ {}_2F_1$-hypergeometric functions as identities among automorphic forms on different Shimura curves.


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Additional Information

Fang-Ting Tu
Affiliation: Department of Applied Mathematics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan 30010, Republic of China
Email: ft12.am95g@nctu.edu.tw

Yifan Yang
Affiliation: Department of Applied Mathematics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan 30010, Republic of China – and – National Center for Theoretical Sciences, Hsinchu 300, Taiwan, Republic of China
Email: yfyang@math.nctu.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05960-0
PII: S 0002-9947(2013)05960-0
Received by editor(s): December 12, 2011
Received by editor(s) in revised form: September 10, 2012
Published electronically: July 26, 2013
Additional Notes: The authors were partially supported by Grant 99-2115-M-009-011-MY3 of the National Science Council, Taiwan (R.O.C.).
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.