Some q -supercongruences related to the (A.3) and (D.3) conjectures of Swisher

In this paper, by making use of the creative microscoping method introduced by Guo and Zudilin [Adv. Math. 346 (2019), 329-358] and the Chinese remainder theorem for coprime polynomials, we establish partial q-analogues of Swisher’s conjectures (A.3) and (D.3), thereby partially confirming them. In particular, we respectively obtain weakened forms of the conjectures proposed by Guo and Zudilin, and by Liu and Wang.