q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
By Ofir Gorodetsky. International Journal of Number Theory, 2018
49 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/ec69d65dc249ea108ef7387018543eb7c6d00460
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In Algebra and Number Theory
- Victor J. W. Guo
- Michael J. Schlosser
- Wadim Zudilin
- Armin Straub
- Ji-Cai Liu
- Ofir Gorodetsky
- Zhi-Guo Liu
- Su-Dan Wang
In Geometry and Topology
Citations in the corpus
- Congruences for q-Binomial Coefficients (2019, background): “ore, it is tempting to expect that these two families of q-congruences may be generalised even further in the spirit of Theorems 1 and 2, and that the polynomials Dn(q) satisfy q-Gauss relations from [4]. We do not pursue this line here. ProofofTheorem 3. Though the congruences (15) and (16) are bet”
- Supercongruences for polynomial analogs of the Apéry numbers (2018, background): “, which is proved in Lemma A.2. Acknowledgements. I am extremely thankful to Ofir Gorodetsky for motivating me to finally complete and write up the present paper, and for sharing a preprint of his work [20] in which he obtains q-congruences, from which he is able to derive the stronger congruences A(p”
- 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]).”