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arXiv · 1805.01254

q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon

Ofir Gorodetsky
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Abstract

We establish a supercongruence conjectured by Almkvist and Zudilin, by proving a corresponding $q$-supercongruence. Similar $q$-supercongruences are established for binomial coefficients and the Apéry numbers, by means of a general criterion involving higher derivatives at roots of unity. Our methods lead us to discover new examples of the cyclic sieving phenomenon, involving the $q$-Lucas numbers.

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Ofir Gorodetsky. 2019-12-01. q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon. https://doi.org/10.1142/s1793042119501069

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