q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
2019 ◽
Vol 15
(09)
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pp. 1919-1968
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Keyword(s):
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.
2004 ◽
Vol 108
(1)
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pp. 17-50
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2011 ◽
Vol DMTCS Proceedings vol. AO,...
(Proceedings)
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Keyword(s):
2010 ◽
Vol DMTCS Proceedings vol. AN,...
(Proceedings)
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2011 ◽
Vol DMTCS Proceedings vol. AO,...
(Proceedings)
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Keyword(s):