Divisibility of certain sums involving central \(q\)-binomial coefficients

DOI10.1216/RMJ.2024.54.1291MaRDI QIDQ6635545

Yifan Chen, Xiaoxia Wang

Publication date: 12 November 2024

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

congruencescyclotomic polynomials\(q\)-binomial coefficients\(q\)-congruences

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) (q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65)

Cites Work

• Title not available (Why is that?)
• Ramanujan-type supercongruences
• Modular equations and approximations to \(\pi\).
• A \(q\)-analogue of a Ramanujan-type supercongruence involving central binomial coefficients
• 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 \(p\equiv 1\pmod{4}\)
• Factors of certain sums involving central \(q\)-binomial coefficients
• Some \(q\)-supercongruences from a quadratic transformation by Rahman
• Further \(q\)-analogues of the (G.2) supercongruence of Van Hamme
• \(q\)-supercongruences on triple and quadruple sums
• A method for proving Ramanujan's series for \(1/\pi\)
• Congruences for \(q\)-binomial coefficients
• Some symmetric \(q\)-congruences modulo the square of a cyclotomic polynomial
• Factors of the Gaussian coefficients
• Some \(q\)-supercongruences from transformation formulas for basic hypergeometric series
• \(q\)-supercongruences from gasper and Rahman's summation formula
• Proofs of Guo and Schlosser's two conjectures
• Divisibility of some binomial sums
• Von den Coefficienten der Reihen von Kugelfunctionen einer Variablen.
• A further q-analogue of Van Hamme’s (H.2) supercongruence for primes p ≡ 3(mod4)
• Two curious \(q\)-supercongruences and their extensions
• Proof of two conjectures of Guo and of Tang

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