On divisibility of sums of Apéry polynomials
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Publication:740380
DOI10.1016/j.jnt.2014.03.006zbMath1353.11004arXiv1108.1546OpenAlexW2082576966MaRDI QIDQ740380
Publication date: 2 September 2014
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1108.1546
Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07) Special sequences and polynomials (11B83)
Related Items (12)
A supercongruence involving Delannoy numbers and Schröder numbers ⋮ Gaussian binomial coefficients modulo cyclotomic polynomials ⋮ On congruences involving Apéry numbers ⋮ On a generalized homogeneous Hahn polynomial ⋮ CONGRUENCES FOR THE TH APÉRY NUMBER ⋮ Factors of alternating sums of powers of \(q\)-Narayana numbers ⋮ Proof of two congruences concerning Legendre polynomials ⋮ Congruences on truncated double summation series ⋮ On the divisibility of sums involving powers of multi-variable Schmidt polynomials ⋮ On two supercongruences involving Almkvist-Zudilin sequences ⋮ Some congruences involving powers of Legendre polynomials ⋮ ON THE DIVISIBILITY OF SUMS INVOLVING APÉRY-LIKE POLYNOMIALS
Cites Work
- Proof of some conjectures of Z.-W. Sun on congruences for Apéry polynomials
- \(q\)-analogs of some congruences involving Catalan numbers
- On sums of Apéry polynomials and related congruences
- Congruences involving generalized central trinomial coefficients
- A generalization of the Gaussian formula and a \(q\)-analog of Fleck's congruence
- A congruence involving products of \(q\)-binomial coefficients
- Congruences for the q-secant numbers
- Some congruences for Apery numbers
- Congruence properties of \(q\)-analogs
- A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
- \(q\)-analogs of the binomial coefficient congruences of Babbage, Wolstenholme and Glaisher
- Generalized \(q\)-Legendre polynomials
- Another congruence for the Apéry numbers
- Some arithmetic properties of the \(q\)-Euler numbers and \(q\)-Salié numbers
- On q-Analog of Wolstenholme Type Congruences for Multiple Harmonic Sums
- NEW CONGRUENCES FOR SUMS INVOLVING APÉRY NUMBERS OR CENTRAL DELANNOY NUMBERS
- Factors of sums of powers of binomial coefficients
- A Gaussian hypergeometric series evaluation and Apéry number congruences
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