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Supercongruences for polynomial analogs of the Apéry numbers


Author: Armin Straub
Journal: Proc. Amer. Math. Soc. 147 (2019), 1023-1036
MSC (2010): Primary 11B65, 05A30; Secondary 11B83
DOI: https://doi.org/10.1090/proc/14301
Published electronically: November 16, 2018
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Abstract: We consider a family of polynomial analogs of the Apéry numbers, which includes $ q$-analogs due to Krattenthaler-Rivoal-Zudilin and Zheng, and show that the supercongruences that Gessel and Mimura established for the Apéry numbers generalize to these polynomials. Our proof relies on polynomial analogs of classical binomial congruences of Wolstenholme and Ljunggren. We further indicate that this approach generalizes to other supercongruence results.


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Additional Information

Armin Straub
Affiliation: Department of Mathematics and Statistics, University of South Alabama, 411 University Boulevard N, MSPB 325, Mobile, Alabama 36688
Email: straub@southalabama.edu

DOI: https://doi.org/10.1090/proc/14301
Received by editor(s): March 20, 2018
Received by editor(s) in revised form: June 25, 2018
Published electronically: November 16, 2018
Communicated by: Amanda Folsom
Article copyright: © Copyright 2018 American Mathematical Society

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