\(q\)-supercongruences from squares of basic hypergeometric series
DOI10.1007/s13398-022-01364-9OpenAlexW4310275919MaRDI QIDQ2681975
Publication date: 31 January 2023
Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2112.12076
basic hypergeometric seriesChinese remainder theoremcyclotomic polynomialtruncated sum\(q\)-supercongruencecreative microscoping method
(q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences; primitive roots; residue systems (11A07)
Related Items (6)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Hypergeometric evaluation identities and supercongruences
- Some \(q\)-analogues of supercongruences of Rodriguez-Villegas
- \(q\)-analogues of two ``divergent Ramanujan-type supercongruences
- On a congruence involving \(q\)-Catalan numbers
- On supercongruences for truncated sums of squares of basic hypergeometric series
- Some supercongruences occurring in truncated hypergeometric series
- A \(q\)-analogue of a Ramanujan-type supercongruence involving central binomial coefficients
- A \(q\)-microscope for supercongruences
- A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function.
- Proof of a \(q\)-supercongruence conjectured by Guo and Schlosser
- 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 \(p\equiv 1\pmod{4}\)
- Some \(q\)-supercongruences from a quadratic transformation by Rahman
- A new extension of the (A.2) supercongruence of Van Hamme
- A variation of the \(q\)-Wolstenholme theorem
- 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
- A new family of \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial
- Some new \(q\)-congruences on double sums
- Proof of a generalization of the (C.2) supercongruence of Van Hamme
- Two \(q\)-congruences involving double basic hypergeometric sums
- Congruences for \(q\)-binomial coefficients
- Congruences on sums of \(q\)-binomial coefficients
- Some symmetric \(q\)-congruences modulo the square of a cyclotomic polynomial
- On a \(q\)-deformation of modular forms
- Some \(q\)-supercongruences from transformation formulas for basic hypergeometric series
- Proofs of Guo and Schlosser's two conjectures
- On the divisibility of \(q\)-trinomial coefficients
- “Divergent” Ramanujan-type supercongruences
- On a conjectured q-congruence of Guo and Zeng
- A q-analogue of the (A.2) supercongruence of Van Hamme for any prime p ≡ 3(mod4)
- Some Transformations of Basic Hypergeometric Functions. Part II
- On q-Analogues of the Watson and Whipple Summations
- Supercongruences for polynomial analogs of the Apéry numbers
- $q$-Supercongruences from the $q$-Saalschütz identity
- Some congruences involving fourth powers of central q-binomial coefficients
- Some q-supercongruences for truncated forms of squares of basic hypergeometric series
- A further q-analogue of Van Hamme’s (H.2) supercongruence for primes p ≡ 3(mod4)
- A TRUNCATED IDENTITY OF EULER AND RELATED -CONGRUENCES
- Some $q$-congruences with parameters
This page was built for publication: \(q\)-supercongruences from squares of basic hypergeometric series
