Some new q-supercongruences modulo the fourth and fifth powers of a cyclotomic polynomial
We give some new [Formula: see text]-supercongruences modulo the fourth and fifth powers of a cyclotomic polynomial, respectively. One of them is related to the following congruence due to Deines, Fuselier, Long, Swisher, and Tu: for primes [Formula: see text], [Formula: see text] where [Formula: see text] denotes the [Formula: see text]-adic Gamma function. Our proof relies on Watson’s [Formula: see text] transformation and the “creative microscoping” method introduced by the first author and Zudilin.
Authors
- Victor J. W. Guo (ORCID: https://orcid.org/0000-0002-4153-715X)
- Jian-Ning Wu (ORCID: https://orcid.org/0009-0003-0455-2910)
Institutions
- Hangzhou Normal University (CN)
Publication Details
- Journal
- International Journal of Number Theory
- Published
- 2026-11-06
- DOI
- https://doi.org/10.1142/s1793042127500254
- Primary Topic
- Advanced Mathematical Identities
- Type
- article
- Field-Weighted Citation Impact
- 0.00