Some \(q\)-supercongruences modulo the fifth power of a cyclotomic polynomial from squares of \(q\)-hypergeometric series
DOI10.1007/s00025-021-01536-wzbMath1490.11006OpenAlexW3213417290MaRDI QIDQ2051427
Publication date: 24 November 2021
Published in: Results in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00025-021-01536-w
\(q\)-hypergeometric seriesChinese remainder theoremcyclotomic polynomialtruncated sum\(q\)-supercongruencecreative microscoping method
Factorials, binomial coefficients, combinatorial functions (05A10) (q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) (zeta (s)) and (L(s, chi)) (11M06) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences; primitive roots; residue systems (11A07) Generalized hypergeometric series, ({}_pF_q) (33C20)
Related Items (3)
Cites Work
- On the supercongruence conjectures of van Hamme
- Hypergeometric evaluation identities and supercongruences
- On a congruence involving \(q\)-Catalan numbers
- On supercongruences for truncated sums of squares of basic hypergeometric series
- A \(p\)-adic analogue of a formula of Ramanujan
- Ramanujan-type supercongruences
- 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 modulo the fourth power of a cyclotomic polynomial
- A further \(q\)-analogue of Van Hamme's (H.2) supercongruence for any prime \(p\equiv 1\pmod{4}\)
- A new extension of the (H.2) supercongruence of Van Hamme for primes \(p\equiv 3\operatorname{mod}{4}\)
- A \(q\)-analogue of the (A.2) supercongruence of Van Hamme for primes \(p\equiv 1\pmod{4} \)
- \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial via creative microscoping
- Dwork-type supercongruences through a creative \(q\)-microscope
- Proof of a generalization of the (C.2) supercongruence of Van Hamme
- Congruences on sums of \(q\)-binomial coefficients
- On a \(q\)-deformation of modular forms
- Some \(q\)-supercongruences from transformation formulas for basic hypergeometric series
- A q-analogue of the (A.2) supercongruence of Van Hamme for any prime p ≡ 3(mod4)
- A $p$-adic supercongruence conjecture of van Hamme
- Some congruences involving fourth powers of central q-binomial coefficients
- Some q-supercongruences for truncated forms of squares of basic hypergeometric series
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