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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Algebraic transformations of hypergeometric functions and automorphic forms on Shimura curves
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by Fang-Ting Tu and Yifan Yang PDF
Trans. Amer. Math. Soc. 365 (2013), 6697-6729 Request permission

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.
References
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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
  • MR Author ID: 633505
  • Email: yfyang@math.nctu.edu.tw
  • 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.).
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 365 (2013), 6697-6729
  • MSC (2010): Primary 11F12; Secondary 11G18, 33C05
  • DOI: https://doi.org/10.1090/S0002-9947-2013-05960-0
  • MathSciNet review: 3105767