Journal article
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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(Accepted manuscript, 561.8KB)
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- Publisher copy:
- 10.1142/s1793042119501069
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Authors
Bibliographic Details
- 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
Item Description
- Language:
- English
- Keywords:
- Pubs id:
-
1145838
- Local pid:
- pubs:1145838
- Deposit date:
- 2020-11-17
Terms of use
- Copyright holder:
- World Scientific Publishing Company
- Copyright date:
- 2019
- Rights statement:
- © World Scientific Publishing Company 2019.
- Notes:
- This is the accepted manuscript version of the article. The final version is available from World Scientific Publications at: https://doi.org/10.1142/S1793042119501069
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