New \(q\)-supercongruences from the Bailey transformation
DOI10.1216/rmj.2022.52.2145OpenAlexW4313233257MaRDI QIDQ2678290
Publication date: 9 January 2023
Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2201.05378
cyclotomic polynomialsbasic hypergeometric seriesRamanujan-type supercongruences\(q\)-congruencescreative microscoping methodBailey transformation formula
(q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Polynomials in number theory (11C08) 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
- Hypergeometric evaluation identities and supercongruences
- Ramanujan's ``lost notebook. IV: Stacks and alternating parity in partitions
- A \(q\)-microscope for supercongruences
- \(q\)-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 a quadratic transformation by Rahman
- A new family of \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial
- \(q\)-analogues of the (E.2) and (F.2) supercongruences of van Hamme
- Some generalizations of a congruence by Sun and Tauraso
- Some \(q\)-supercongruences from the Bailey transformation
- Some q-analogs of congruences for central binomial sums
- Divisibility of some binomial sums
- Some congruences on truncated hypergeometric series
- $q$-Supercongruences from the $q$-Saalschütz identity
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