Some $q$-analogs of congruences for central binomial sums

By Roberto Tauraso. 2012

69 citations recorded by the source corpus.

We establish $q$-analogs for four congruences involving central binomial coefficients. The $q$-identities necessary for this purpose are shown via the $q$-WZ method.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/34db5d2bf8d55c1d05f98c198b6e400d59a93e2e

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In Algebra and Number Theory

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

A family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial (2019, background): “During the past few years, many congruences and supercongruences were generalized to the q-setting by various authors (see, for instance, [5–18, 25, 26, 30, 32]).”
Some congruences related to a congruence of Van Hamme (2019, methodology): “For more supercongruences and q-supercongruences, we refer the reader to [4, 6–20, 26, 29, 30].”
Some q-Supercongruences from Transformation Formulas for Basic Hypergeometric Series (2018, background): “We refer the reader to [1, 8, 18, 26, 36, 40, 41] for some interesting q-congruences.”
On a congruence involving $q$-Catalan numbers (2019, background): “In the past few years, q-analogues of congruences (q-congruence) for indefinite sums of binomial coefficients as well as hypergeometric series attracted many experts’ attention (see, for example, [2–6,9,10]).”