Supercongruences between truncated 2F1 hypergeometric functions and their Gaussian analogs
Supercongruences between truncated 2F1 hypergeometric functions and their Gaussian analogs
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DOI：
10.1090/s0002-9947-02-03172-0
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发表时间：
2002-10
影响因子：
1.3
通讯作者：
Eric T. Mortenson
中科院分区：
文献类型：
--
作者：
Eric T. Mortenson
Fernando Rodriguez-Villegas证明了维数d < 3的超几何Calabi-Yau流形的超同余。对于维数d = 1的流形，他观察到四个潜在的超同余。后来，作者证明了这四个之一。受Rodriguez-Villegas工作的启发，本文证明了截断2F 1超几何函数与Gauss超几何函数值之间的超同余关系的一个一般结果.作为该结果的推论，我们证明了剩余的三个超全等。
Fernando Rodriguez-Villegas has conjectured a number of supercongruences for hypergeometric Calabi-Yau manifolds of dimension d < 3. For manifolds of dimension d = 1, he observed four potential supercongruences. Later the author proved one of the four. Motivated by Rodriguez-Villegas's work, in the present paper we prove a general result on supercongruences between values of truncated 2 F 1 hypergeometric functions and Gaussian hypergeometric functions. As a corollary to that result, we prove the three remaining supercongruences.