A -ANALOGUE OF A DWORK-TYPE SUPERCONGRUENCE

DOI10.1017/S0004972720000635zbMath1476.11007OpenAlexW3042424828MaRDI QIDQ5857597

Mingbing Yue, Xiaoxia Wang

Publication date: 1 April 2021

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972720000635

zbMATH Keywords

\(q\)-congruence\(q\)-analoguebasic hypergeometric seriescombinatorial congruence

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences; primitive roots; residue systems (11A07)

Related Items (19)

Proof of two conjectures of Guo and Schlosser ⋮ A \(q\)-Dwork-type generalization of Rodriguez-Villegas' supercongruences ⋮ On a generalization of a congruence related to \(q\)-Narayana numbers ⋮ A FAMILY OF -SUPERCONGRUENCES MODULO THE CUBE OF A CYCLOTOMIC POLYNOMIAL ⋮ Some \(q\)-analogues of supercongruences for truncated \({}_3 F_2\) hypergeometric series ⋮ Proofs of Guo and Schlosser's two conjectures ⋮ Proof of some supercongruences through a \(q\)-microscope ⋮ Some \(q\)-supercongruences from squares of basic hypergeometric series ⋮ \(q\)-analogues of the (G.2) supercongruence of Van Hamme ⋮ Two \(q\)-congruences involving double basic hypergeometric sums ⋮ Supercongruences for sums involving Domb numbers ⋮ \(q\)-analogues of two Ramanujan-type supercongruences ⋮ Another family of \(q\)-congruences modulo the square of a cyclotomic polynomial ⋮ $q$-Supercongruences from the $q$-Saalschütz identity ⋮ Some \(q\)-supercongruences modulo the square and cube of a cyclotomic polynomial ⋮ On two supercongruences for sums of Apéry-like numbers ⋮ Some \(q\)-supercongruences from a quadratic transformation by Rahman ⋮ \(q\)-supercongruences from transformation formulas ⋮ Further \(q\)-analogues of the (G.2) supercongruence of Van Hamme

Cites Work

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• On the supercongruence conjectures of van Hamme
• Hypergeometric evaluation identities and supercongruences
• Ramanujan-type supercongruences
• A \(q\)-microscope for supercongruences
• \(q\)-analogues of three Ramanujan-type formulas for \(1/\pi\)
• Some \(q\)-supercongruences from Watson's \(_8\phi_7\) transformation formula
• A \(q\)-analogue of the (A.2) supercongruence of Van Hamme for primes \(p\equiv 1\pmod{4} \)
• Dwork-type supercongruences through a creative \(q\)-microscope
• Congruences for \(q\)-binomial coefficients
• Congruences on sums of \(q\)-binomial coefficients
• \(q\)-analogues of Dwork-type supercongruences
• Common \(q\)-analogues of some different supercongruences
• A q-analogue of the (A.2) supercongruence of Van Hamme for any prime p ≡ 3(mod4)
• Some congruences on truncated hypergeometric series
• A $p$-adic supercongruence conjecture of van Hamme

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