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q-Supercongruences from Jackson's ϕ78 summation and Watson's ϕ78 transformation
Journal of Combinatorial Theory Series A ( IF 0.9 ) 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 ϕ78 summation, Watson's ϕ78 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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