\(q\)-supercongruences from Jackson's \({}_8 \phi_7\) summation and Watson's \({}_8 \phi_7\) transformation
DOI10.1016/j.jcta.2023.105853arXiv2104.07025OpenAlexW4390829971MaRDI QIDQ6201498
Publication date: 21 February 2024
Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2104.07025
cyclotomic polynomialsbasic hypergeometric seriesChinese remainder theoremcreative microscoping method\(q\)-supercongruencesJackson's \({}_8\phi _7\) summationWatson's \({}_8\phi _7\) transformation
(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
- Unnamed Item
- Unnamed Item
- Unnamed Item
- \(q\)-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
- Some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial
- Further \(q\)-analogues of the (G.2) supercongruence of Van Hamme
- \(q\)-supercongruences on triple and quadruple sums
- A family of \(q\)-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial
- Dwork-type supercongruences through a creative \(q\)-microscope
- Two \(q\)-supercongruences from Watson's transformation
- Congruences for \(q\)-binomial coefficients
- Congruences on sums of \(q\)-binomial coefficients
- \(q\)-analogues of the (E.2) and (F.2) supercongruences of van Hamme
- Some \(q\)-supercongruences from transformation formulas for basic hypergeometric series
- An extension of a supercongruence of Long and Ramakrishna
This page was built for publication: \(q\)-supercongruences from Jackson's \({}_8 \phi_7\) summation and Watson's \({}_8 \phi_7\) transformation
