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

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.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1142/s1793042119501069

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
World Scientific Publisher's website
Journal:
International Journal of Number Theory Journal website
Volume:
15
Issue:
09
Pages:
1919-1968
Publication date:
2019-10-03
Acceptance date:
2019-04-11
DOI:
EISSN:
1793-7310
ISSN:
1793-0421
Language:
English
Keywords:
Pubs id:
1145838
Local pid:
pubs:1145838
Deposit date:
2020-11-17

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