Supercongruences for truncated \({}_{n+1}F_{n}\) hypergeometric series with applications to certain weight three newforms. (English) Zbl 1152.11327
Summary: We prove general results on supercongruences between values of truncated \(_{n+1}F_{n}\) hypergeometric functions and their character analogs. As a consequence of the main results of this paper, we prove Beukers-type supercongruences for certain weight three newforms.
MSC:
| 11F33 | Congruences for modular and \(p\)-adic modular forms |
| 11S80 | Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.) |
| 11L05 | Gauss and Kloosterman sums; generalizations |
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