Supercongruences between truncated ₂𝐹₁ hypergeometric functions and their Gaussian analogs

Mortenson, Eric

doi:10.1090/S0002-9947-02-03172-0

Supercongruences between truncated $_{2}F_{1}$ hypergeometric functions and their Gaussian analogs
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Trans. Amer. Math. Soc. 355 (2003), 987-1007 Request permission

Abstract:

Fernando Rodriguez-Villegas has conjectured a number of supercongruences for hypergeometric Calabi-Yau manifolds of dimension $d\le 3$. 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.

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