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Supercongruences for polynomial analogs of the Apéry numbers

Supercongruences for polynomial analogs of the Apéry numbers
Armin Straub — Proceedings of the American Mathematical Society — Volume 147, 2019, Pages 1023-1036

Abstract

We consider a family of polynomial analogs of the Apéry numbers, which includes \(q\)-analogs of 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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BibTeX

@article{qapery-2019,
    author = {Armin Straub},
    title = {Supercongruences for polynomial analogs of the Ap\'ery numbers},
    journal = {Proceedings of the American Mathematical Society},
    year = {2019},
    volume = {147},
    pages = {1023--1036},
    doi = {10.1090/proc/14301},
}