q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
Number Theory
2019-12-03 v2 Combinatorics
Abstract
We establish a supercongruence conjectured by Almkvist and Zudilin, by proving a corresponding -supercongruence. Similar -supercongruences are established for binomial coefficients and the Ap\'{e}ry 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 -Lucas numbers.
Keywords
Cite
@article{arxiv.1805.01254,
title = {q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon},
author = {Ofir Gorodetsky},
journal= {arXiv preprint arXiv:1805.01254},
year = {2019}
}
Comments
Incorporated comments from referees. Accepted for publication in Int. J. Number Theory