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\((q)\)-supercongruences hit again. (English) Zbl 1472.11029
Summary: Using an intrinsic \(q\)-hypergeometric strategy, we generalise Dwork-type congruences \(H(p^{s+1})/H(p^s)\equiv H(p^s)/H(p^{s-1}) \pmod{p^3}\) for \(s=1,2,\ldots\) and \(p\) a prime, when \(H(N)\) are truncated hypergeometric sums corresponding to the periods of rigid Calabi-Yau threefolds.
MSC:
11A07 Congruences; primitive roots; residue systems
11B65 Binomial coefficients; factorials; \(q\)-identities
11F33 Congruences for modular and \(p\)-adic modular forms
33C20 Generalized hypergeometric series, \({}_pF_q\)
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
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