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On a conjectured \(q\)-congruence of Guo and Zeng. (English) Zbl 1428.11041


MSC:

11B65 Binomial coefficients; factorials; \(q\)-identities
11A07 Congruences; primitive roots; residue systems
05A10 Factorials, binomial coefficients, combinatorial functions
05A30 \(q\)-calculus and related topics
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References:

[1] Andrews, G. E., The Theory of Partitions, (1998), Cambridge University Press, Cambridge · Zbl 0996.11002
[2] Guo, V. J. W.; Pan, H.; Zhang, Y., The rodriguez-villegas type congruences for truncated \(q\)-hypergeometric functions, J. Number Theory, 174, 358-368, (2017) · Zbl 1387.11018
[3] Guo, V. J. W.; Zeng, J., Some \(q\)-analogues of supercongruences of rodriguez-villegas, J. Number Theory, 145, 301-316, (2014) · Zbl 1315.11015
[4] Guo, V. J. W.; Zeng, J., Some \(q\)-supercongruences for truncated basic hypergeometric series, Acta Arith., 1171, 309-326, (2015) · Zbl 1338.11024
[5] Mortenson, E., A supercongruence conjecture of rodriguez-villegas for a certain truncated hypergeometric function, J. Number Theory, 199, 139-147, (2003) · Zbl 1074.11045
[6] Mortenson, E., Supercongruences between truncated \({}_2 F_1\) hypergeometric functions and their Gaussian analogs, Trans. Amer. Math. Soc., 1355, 987-1007, (2003) · Zbl 1074.11044
[7] Rodriguez-Villegas, F., Calabi-Yau Varieties and Mirror Symmetry, 38, Hypergeometric families of Calabi-Yau manifolds, 223-231, (2003), American Mathematical Society, Providence, RI · Zbl 1062.11038
[8] Sun, Z.-H., Generalized Legendre polynomials and related supercongruences, J. Number Theory, 143, 293-319, (2014) · Zbl 1353.11005
[9] Sun, Z.-H., Supecongruences involving products of two binomial coefficients, Finite Fields Appl., 122, 24-44, (2013) · Zbl 1331.11012
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