q-Supercongruences from Jackson's ϕ78 summation and Watson's ϕ78 transformation,Journal of Combinatorial Theory Series A

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q-Supercongruences from Jackson's ϕ78 summation and Watson's ϕ78 transformation
Journal of Combinatorial Theory Series A ( IF 1.1 ) Pub Date : 2024-01-12 , DOI: 10.1016/j.jcta.2023.105853
Chuanan Wei

q-Supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial are very rare in the literature. In this paper, we establish some q-supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial in terms of Jackson's ${}_{8}ϕ_{7}$ summation, Watson's ${}_{8}ϕ_{7}$ transformation, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials. More concretely, we give a q-analogue of a nice formula due to Long and Ramakrishna [Adv. Math. 290 (2016), 773–808] and two q-supercongruences involving double series.

更新日期：2024-01-14

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