Some q-supercongruences related to Swisher’s (H.3) conjecture

DOI10.1142/S1793042122500725zbMath1502.33007OpenAlexW4200010656WikidataQ113776642 ScholiaQ113776642MaRDI QIDQ5082473

Jian-Ping Fang, Victor J. W. Guo

Publication date: 16 June 2022

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042122500725

zbMATH Keywords

cyclotomic polynomial\(p\)-adic Gamma functionWatson's transformation\(q\)-Dixon sum\(q\)-supercongruences

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)

Cites Work

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• On the supercongruence conjectures of van Hamme
• On sums of Apéry polynomials and related congruences
• Generalized Legendre polynomials and related supercongruences
• A family of \(q\)-congruences modulo the square of a cyclotomic polynomial
• On a congruence involving \(q\)-Catalan numbers
• Some supercongruences occurring in truncated hypergeometric series
• On Van Hamme's (A.2) and (H.2) supercongruences
• A \(q\)-microscope for supercongruences
• \(q\)-analogues of two Ramanujan-type supercongruences
• Some \(q\)-supercongruences from Watson's \(_8\phi_7\) transformation formula
• A common \(q\)-analogue of two supercongruences
• 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
• Some symmetric \(q\)-congruences modulo the square of a cyclotomic polynomial
• On some conjectures of Swisher
• On a \(q\)-deformation of modular forms
• A q-analogue of the (A.2) supercongruence of Van Hamme for any prime p ≡ 3(mod4)
• Some q-supercongruences for truncated basic hypergeometric series
• q-Analogues of two Ramanujan-type formulas for 1/π
• Some variations of a ‘divergent’ Ramanujan-type q-supercongruence
• A further q-analogue of Van Hamme’s (H.2) supercongruence for primes p ≡ 3(mod4)
• A FAMILY OF -SUPERCONGRUENCES MODULO THE CUBE OF A CYCLOTOMIC POLYNOMIAL
• Some supercongruences on truncated hypergeometric series

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