Some q-supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial

The research of supercongruences has a long history in the literature. Theexploration of q-supercongruences attracts many people's attention recently. In this paper, we establish several q-supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial in terms of several summation and transformation formulas for basic hypergeometric series, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials. More concretely,we give a q-supercongruence related to Van Hamme's (A.2) conjecture, a q-analogue of a nice formula due to Long and Ramakrishna [Adv. Math. 290 (2016), 773--808],and some q-supercongruences involving double series.