A q-analogue of the (I.2) supercongruence of Van Hamme
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Publication:4623460
DOI10.1142/S1793042118501701zbMath1461.11037OpenAlexW2884027099WikidataQ129558228 ScholiaQ129558228MaRDI QIDQ4623460
Publication date: 15 February 2019
Published in: International Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s1793042118501701
\(q\)-analoguescyclotomic polynomials\(q\)-Gamma functionRamanujan-type supercongruences\(q\)-binomial coefficients
Factorials, binomial coefficients, combinatorial functions (05A10) (q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07)
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On a \(q\)-deformation of modular forms ⋮ Factors of some truncated basic hypergeometric series ⋮ Some \(q\)-congruences arising from certain identities ⋮ A \(q\)-analogue of the (A.2) supercongruence of Van Hamme for primes \(p\equiv 1\pmod{4} \) ⋮ On two double series for \(\pi\) and their \(q\)-analogues ⋮ A family of \(q\)-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial ⋮ \(q\)-analogues of the (G.2) supercongruence of Van Hamme ⋮ \(q\)-analogues of two Ramanujan-type supercongruences ⋮ $q$-analogues of several $\pi $-formulas ⋮ A symmetric formula for hypergeometric series ⋮ Some congruences related to a congruence of Van Hamme ⋮ Some new \(q\)-congruences for truncated basic hypergeometric series: even powers ⋮ \(q\)-analogues of Dwork-type supercongruences ⋮ Some new \(q\)-congruences for truncated basic hypergeometric series ⋮ Common \(q\)-analogues of some different supercongruences ⋮ Proof of a basic hypergeometric supercongruence modulo the fifth power of a cyclotomic polynomial
Cites Work
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- \(q\)-analogue of a binomial coefficient congruence
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- A generalization of Morley's congruence
- \(q\)-analogues of the (E.2) and (F.2) supercongruences of van Hamme
- Congruence properties of ordinary and q-binomial coefficients
- Some q-analogs of congruences for central binomial sums
- Some q-supercongruences for truncated basic hypergeometric series
- A $p$-adic supercongruence conjecture of van Hamme
- Some congruences involving fourth powers of central q-binomial coefficients
