$q$-analogues of two supercongruences of Z.-W. Sun

DOI10.21136/CMJ.2020.0516-18MaRDI QIDQ5122220

Victor J. W. Guo, Cheng-Yang Gu

Publication date: 22 September 2020

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

congruences\(q\)-binomial coefficientcyclotomic polynomialFranklin's involution

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) (q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07)

Related Items (13)

Two \(q\)-congruences from Carlitz's formula ⋮ A common \(q\)-analogue of two supercongruences ⋮ A \(q\)-analogue of the (A.2) supercongruence of Van Hamme for primes \(p\equiv 1\pmod{4} \) ⋮ Proof of some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial ⋮ Further generalizations of four supercongruences of Rodriguez-Villegas ⋮ A TRUNCATED IDENTITY OF EULER AND RELATED -CONGRUENCES ⋮ PROOF OF TWO CONJECTURES ON SUPERCONGRUENCES INVOLVING CENTRAL BINOMIAL COEFFICIENTS ⋮ Proof of a supercongruence conjectured by Sun through a \(q\)-microscope ⋮ Congruences on sums of \(q\)-binomial coefficients ⋮ Proof of a generalization of the (B.2) supercongruence of Van Hamme through a \(q\)-microscope ⋮ \(q\)-analogues of Dwork-type supercongruences ⋮ On the divisibility of sums of even powers of \(q\)-binomial coefficients ⋮ Truncations of Gauss' square exponent theorem

Cites Work

• Unnamed Item
• Fibonacci numbers modulo cubes of primes
• Lattice paths and positive trigonometric sums
• A new class of \(q\)-Fibonacci polynomials
• Some finite generalizations of Gauss's square exponent identity
• Factors of sums and alternating sums of products of \(q\)-binomial coefficients and powers of \(q\)-integers
• A \(q\)-microscope for supercongruences
• Some observations on Dyson's new symmetries of partitions
• The number of solutions of \(X^ 2 = 0\) in triangular matrices over \(GF(q)\)
• Common \(q\)-analogues of some different supercongruences
• NEW CONGRUENCES FOR SUMS INVOLVING APÉRY NUMBERS OR CENTRAL DELANNOY NUMBERS
• q-Analogues of two Ramanujan-type formulas for 1/π
• Some finite generalizations of Euler's pentagonal number theorem
• A New Proof of Rogers's Transformations of Infinite Series

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