Supercongruences for the Almkvist–Zudilin numbers

DOI10.4064/aa8215-2-2016zbMath1360.11004arXiv1506.08437OpenAlexW2963072603MaRDI QIDQ3178174

Roberto Tauraso, Tewodoros Amdeberhane

Publication date: 8 July 2016

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.08437

zbMATH Keywords

congruencesbinomial coefficientsharmonic numbersFermat quotientsAlmkvist-Zudilin numbers

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07) Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (9)

New Representations for all Sporadic Apéry-Like Sequences, With Applications to Congruences ⋮ Gessel-Lucas congruences for sporadic sequences ⋮ CONGRUENCES FOR THE TH APÉRY NUMBER ⋮ Supercongruences for polynomial analogs of the Apéry numbers ⋮ Sequences, modular forms and cellular integrals ⋮ q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon ⋮ Some supercongruences on truncated hypergeometric series ⋮ On two supercongruences involving Almkvist-Zudilin sequences ⋮ Ramanujan-type supercongruences involving Almkvist-Zudilin numbers

Cites Work

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• Multivariate Apéry numbers and supercongruences of rational functions
• Some congruences for the Apéry numbers
• Congruences via Abelian groups
• On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson
• Supercongruences for sporadic sequences
• Supercongruences for a truncated hypergeometric series
• Supercongruences between truncated $_{2}F_{1}$ hypergeometric functions and their Gaussian analogs
• Congruences via modular forms
• CONGRUENCES SATISFIED BY APÉRY-LIKE NUMBERS

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