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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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