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In terms of the creative microscoping method, El Bachraoui's lemmas, and the Chinese remainder theorem for coprime polynomials, we establish some q-supercongruences for double and triple basic hypergeometric series. Several related conjectures are also proposed for further research. [ABSTRACT FROM AUTHOR]

In terms of the q-Saalschütz identity, the creative microscoping method recently introduced by Guo and Zudilin [Adv. Math. 346 (2019), pp. 329–358], and the Chinese remainder theorem for coprime polynomials, we establish some q-supercongruences modulo the third power of a cyclotomic polynomial. In particular, we give a q-analogue of a formula due to Long and Ramakrishna [Adv. Math. 290 (2016), pp. 773–808]. [ABSTRACT FROM AUTHOR]

We give a short proof of the Hou-Sun identity using a q-hypergeometric summation. Furthermore, q-analogues of several other π-formulas are also established according to the q-hypergeometric summations and transformations and the telescoping method. [ABSTRACT FROM AUTHOR]