A further q-analogue of Van Hamme's (H.2) supercongruence for primes p ≡ 3 (mod 4)

Long and Ramakrishna [Some supercongruences occurring in truncated hyper- geometric series, Adv. Math. 290 (2016) 773-808] generalized the (H.2) supercongruence of Van Hamme to the modulus p(3) case. In this paper, we give a q-analogue of Long and Ramakrishna's result for p equivalent to 3 (mod 4). A q-congruence modulo the fourth power of a cyclotomic polynomial, which is a deeper q-analogue of the (A.2) supercongruence of Van Hamme for p equivalent to 3 (mod 4), is also formulated.