q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
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Publication:5236485
DOI10.1142/S1793042119501069zbMath1423.11043arXiv1805.01254WikidataQ127889874 ScholiaQ127889874MaRDI QIDQ5236485
Publication date: 8 October 2019
Published in: International Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1805.01254
(q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07) Special sequences and polynomials (11B83)
Related Items (32)
Two \(q\)-congruences from Carlitz's formula ⋮ Proof of two conjectures of Guo and Schlosser ⋮ A variation of the \(q\)-Wolstenholme theorem ⋮ A common \(q\)-analogue of two supercongruences ⋮ Proof of some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial ⋮ New Representations for all Sporadic Apéry-Like Sequences, With Applications to Congruences ⋮ Some \(q\)-supercongruences from the Bailey transformation ⋮ Gessel-Lucas congruences for sporadic sequences ⋮ \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial via creative microscoping ⋮ On the divisibility of \(q\)-trinomial coefficients ⋮ Cyclic sieving, skew Macdonald polynomials and Schur positivity ⋮ A new family of \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial ⋮ Some new \(q\)-congruences on double sums ⋮ A family of \(q\)-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial ⋮ Dwork-type supercongruences through a creative \(q\)-microscope ⋮ Proof of a generalization of the (C.2) supercongruence of Van Hamme ⋮ Divisibility of some binomial sums ⋮ Supercongruences for polynomial analogs of the Apéry numbers ⋮ Proof of a supercongruence conjectured by Sun through a \(q\)-microscope ⋮ Parity-Unimodality and a Cyclic Sieving Phenomenon for Necklaces ⋮ Congruences for \(q\)-binomial coefficients ⋮ Some \(q\)-supercongruences modulo the square and cube of a cyclotomic polynomial ⋮ Proof of a generalization of the (B.2) supercongruence of Van Hamme through a \(q\)-microscope ⋮ Some new \(q\)-congruences for truncated basic hypergeometric series: even powers ⋮ \(q\)-analogues of Dwork-type supercongruences ⋮ Common \(q\)-analogues of some different supercongruences ⋮ Some \(q\)-supercongruences from a quadratic transformation by Rahman ⋮ Some q-supercongruences for truncated forms of squares of basic hypergeometric series ⋮ The cyclic sieving phenomenon on circular Dyck paths ⋮ Dold sequences, periodic points, and dynamics ⋮ On the divisibility of sums of even powers of \(q\)-binomial coefficients ⋮ A new extension of the (H.2) supercongruence of Van Hamme for primes \(p\equiv 3\operatorname{mod}{4}\)
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