Affiliation:
1. Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 6997801, Israel
Abstract
We establish a supercongruence conjectured by Almkvist and Zudilin, by proving a corresponding [Formula: see text]-supercongruence. Similar [Formula: see text]-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 [Formula: see text]-Lucas numbers.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
30 articles.
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