Some q-supercongruences for double basic hypergeometric series

In terms of the creative microscoping method, El Bachraoui’s lemma, and the Chinese remainder theorem for coprime polynomials, we establish some q -supercongruences for double basic hypergeometric series modulo the fifth and fourth powers of a cyclotomic polynomial. Several related conjectures are also proposed for further research. AMS Subject Classifications: 11A07, 11B65