Proofs of Guo and Schlosser's two conjectures

DOI10.1007/s10998-022-00452-yOpenAlexW4221026315WikidataQ113900768 ScholiaQ113900768MaRDI QIDQ2678446

Chang Xu, Xiaoxia Wang

Publication date: 23 January 2023

Published in: Periodica Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10998-022-00452-y

zbMATH Keywords

basic hypergeometric series\(q\)-congruences\(q\)-supercongruencesJackson's \(_6\phi_5\) summation formula

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 (15)

\(q\)-supercongruences from gasper and Rahman's summation formula ⋮ A new \(q\)-supercongruence modulo the fourth power of a cyclotomic polynomial ⋮ Some \(q\)-supercongruences from the Gasper and Rahman quadratic summation ⋮ Some new results about 𝑞-trinomial coefficients ⋮ Three families of \(q\)-supercongruences modulo the square and cube of a cyclotomic polynomial ⋮ \(q\)-supercongruences from squares of basic hypergeometric series ⋮ Further generalizations of four supercongruences of Rodriguez-Villegas ⋮ Some congruences that extend Van Hamme's (D.2) supercongruence ⋮ Some \(q\)-supercongruences related to Van Hamme's (C.2) supercongruence ⋮ A GENERALISATION OF A SUPERCONGRUENCE ON THE TRUNCATED APPELL SERIES ⋮ New \(q\)-analogues of Van Hamme's (E.2) supercongruence and of a supercongruence by Swisher ⋮ Unnamed Item ⋮ Further \(q\)-analogues of the (G.2) supercongruence of Van Hamme ⋮ Further \(q\)-supercongruences from the \(q\)-Pfaff-Saalschütz identity ⋮ \(q\)-supercongruences on triple and quadruple sums

Cites Work

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• Hypergeometric evaluation identities and supercongruences
• A \(q\)-microscope for supercongruences
• \(q\)-analogues of the (G.2) supercongruence of Van Hamme
• Supercongruences arising from transformations of hypergeometric series
• Proof of a \(q\)-supercongruence conjectured by Guo and Schlosser
• Some \(q\)-supercongruences from a quadratic transformation by Rahman
• Proof of two conjectures of Guo and Schlosser
• \(q\)-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
• Congruences for \(q\)-binomial coefficients
• Some symmetric \(q\)-congruences modulo the square of a cyclotomic polynomial
• Some \(q\)-supercongruences from transformation formulas for basic hypergeometric series
• Some q-analogs of congruences for central binomial sums
• Supercongruences for polynomial analogs of the Apéry numbers
• q-Analogues of two Ramanujan-type formulas for 1/π
• Some congruences involving fourth powers of central q-binomial coefficients
• A -ANALOGUE OF A DWORK-TYPE SUPERCONGRUENCE

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