Further \(q\)-supercongruences from the \(q\)-Pfaff-Saalschütz identity

DOI10.1007/s00025-022-01772-8OpenAlexW4307573122MaRDI QIDQ2093075

Victor J. W. Guo, Cheng-Yang Gu

Publication date: 4 November 2022

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-022-01772-8

zbMATH Keywords

\(p\)-adic gamma function\(q\)-Pfaff-Saalschütz identitycreative microscoping\(q\)-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

• On supercongruences for truncated sums of squares of basic hypergeometric series
• Some supercongruences occurring in truncated hypergeometric series
• A \(q\)-microscope for supercongruences
• Some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial
• Some \(q\)-supercongruences from a quadratic transformation by Rahman
• On the divisibility of sums of even powers of \(q\)-binomial coefficients
• A new extension of the (A.2) supercongruence of Van Hamme
• A variation of the \(q\)-Wolstenholme theorem
• Congruences on sums of \(q\)-binomial coefficients
• Factors of some truncated basic hypergeometric series
• Proofs of Guo and Schlosser's two conjectures
• $q$-Supercongruences from the $q$-Saalschütz identity
• A FAMILY OF -SUPERCONGRUENCES MODULO THE CUBE OF A CYCLOTOMIC POLYNOMIAL
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