$q$-Supercongruences from the $q$-Saalschütz identity

DOI10.1090/proc/15623zbMath1494.33015arXiv2009.03889OpenAlexW3158846901MaRDI QIDQ4957673

Chuanan Wei, Yudong Liu, Xiaoxia Wang

Publication date: 9 September 2021

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.03889

zbMATH Keywords

basic hypergeometric series\(q\)-supercongruencecreative microscoping methodChinese remainder theorem for coprime polynomials\(q\)-Saalschütz identity

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences; primitive roots; residue systems (11A07)

Related Items (4)

New \(q\)-supercongruences from the Bailey transformation ⋮ \(q\)-supercongruences from squares of basic hypergeometric series ⋮ Two \(q\)-operational equations and Hahn polynomials ⋮ Further \(q\)-supercongruences from the \(q\)-Pfaff-Saalschütz identity

Cites Work

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• On the supercongruence conjectures of van Hamme
• \(q\)-analogs of some congruences involving Catalan numbers
• Some supercongruences occurring in truncated hypergeometric series
• A \(q\)-microscope for supercongruences
• Proof of a \(q\)-supercongruence conjectured by Guo and Schlosser
• \(q\)-analogues of two Ramanujan-type supercongruences
• A further \(q\)-analogue of Van Hamme's (H.2) supercongruence for any prime \(p\equiv 1\pmod{4}\)
• Some \(q\)-supercongruences from Watson's \(_8\phi_7\) transformation formula
• Proof of some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial
• \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial via creative microscoping
• A new family of \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial
• Some new \(q\)-congruences on double sums
• A family of \(q\)-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial
• Congruences for \(q\)-binomial coefficients
• Congruences on sums of \(q\)-binomial coefficients
• Factors of some truncated basic hypergeometric series
• Some \(q\)-supercongruences from transformation formulas for basic hypergeometric series
• A q-analogue of the (A.2) supercongruence of Van Hamme for any prime p ≡ 3(mod4)
• Congruences concerning truncated hypergeometric series
• A -ANALOGUE OF A DWORK-TYPE SUPERCONGRUENCE

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