Supercongruences for polynomial analogs of the Apéry numbers
By Armin Straub. Proceedings of the American Mathematical Society, 2018
70 citations recorded by the source corpus.
We consider a family of polynomial analogs of the Ap\'ery numbers, which includes $q$-analogs of Krattenthaler--Rivoal--Zudilin and Zheng, and show that the supercongruences that Gessel and Mimura established for the Ap\'ery 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.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/ccf071e8c8d86c9ba9321ecc478a9e99a2555a28
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In Algebra and Number Theory
- Michael J. Schlosser
- Victor J. W. Guo
- Ofir Gorodetsky
- Wadim Zudilin
- Zhi-Guo Liu
- Ji-Cai Liu
- Jeremy Lovejoy
- V. Spiridonov
In Discrete Mathematics and Combinatorics
Citations in the corpus
- q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon (2018, methodology): “As demonstrated in recent works of Guo and Zudilin [GZ18] and Straub [Str18], the approach of establishing congruences via q-congruences is fruitful because of additional techniques available in the q-setting.”
- A family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial (2019, background): “During the past few years, many congruences and supercongruences were generalized to the q-setting by various authors (see, for instance, [5–18, 25, 26, 30, 32]).”