Some q-supercongruences from a q-analogue of Watson's 3 F 2 summation

Abstract

We give some q-supercongruences from a q-analogue of Watson’s F 2 3 {{}_{3}F_{2}} summation and the method of “creative microscoping”, introduced by the author and Zudilin. These q-supercongruences may be considered as further generalizations of the (A.2) supercongruence of Van Hamme modulo p 3 {p^{3}} or p 2 {p^{2}} for any odd prime p. Meanwhile, we confirm a supercongruence conjecture of Wang and Yue through establishing its q-analogue.