($q$-)Supercongruences hit again

zbMATH Open1472.11029arXiv2011.12084MaRDI QIDQ5011702

Wadim Zudilin

Publication date: 27 August 2021

Abstract: Using an intrinsic $q$-hypergeometric strategy, we generalise Dwork-type congruences $H(p^{s+1})/H(p^s)equivH(p^s)/H(p^{s-1})pmod{p}^3$ for $s=1,2,dots$ and $p$ a prime, when $H(N)$ are truncated hypergeometric sums corresponding to the periods of rigid Calabi--Yau threefolds.

Full work available at URL: https://arxiv.org/abs/2011.12084

zbMATH Keywords

\(q\)-congruencemodular formsupercongruencerigid Calabi-Yau threefoldhypergeometric sumcreative microscopingRamanujan's mathematics

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences for modular and (p)-adic modular forms (11F33) Congruences; primitive roots; residue systems (11A07) Generalized hypergeometric series, ({}_pF_q) (33C20)

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