Some $q$-congruences with parameters

DOI10.4064/aa180624-16-12zbMath1459.11052arXiv1804.10963OpenAlexW2965188206MaRDI QIDQ5237110

Victor J. W. Guo

Publication date: 16 October 2019

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

Full work available at URL: https://arxiv.org/abs/1804.10963

zbMATH Keywords

cyclotomic polynomialsq-binomial coefficientsq-congruencesleast non-negative residue

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences; primitive roots; residue systems (11A07)

Related Items (17)

A \(q\)-Dwork-type generalization of Rodriguez-Villegas' supercongruences ⋮ On a \(q\)-deformation of modular forms ⋮ Factors of some truncated basic hypergeometric series ⋮ Some \(q\)-analogues of supercongruences for truncated \({}_3 F_2\) hypergeometric series ⋮ Congruences concerning generalized central trinomial coefficients ⋮ \(q\)-supercongruences from squares of basic hypergeometric series ⋮ Further generalizations of four supercongruences of Rodriguez-Villegas ⋮ Proof of some supercongruences through a \(q\)-microscope ⋮ A family of \(q\)-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial ⋮ Dwork-type supercongruences through a creative \(q\)-microscope ⋮ Some congruences related to a congruence of Van Hamme ⋮ Some new \(q\)-congruences for truncated basic hypergeometric series: even powers ⋮ On two conjectural supercongruences of Z.-W. Sun ⋮ Common \(q\)-analogues of some different supercongruences ⋮ Some symmetric \(q\)-congruences modulo the square of a cyclotomic polynomial ⋮ \(q\)-analogues of two ``divergent Ramanujan-type supercongruences ⋮ Supercongruences and binary quadratic forms

Cites Work

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