Some symmetric q-congruences modulo the square of a cyclotomic polynomial

Z.-H. Sun (2014) proved a symmetric congruence Sigma(p-1)(k=0)((alpha)(k)) ((-1-alpha)(k))fk (math) (-1)(<alpha > p)Sigma(p-1)(k=0)((alpha)(k)) ((-1-alpha)(k))(f) over cap k (mod p(2)), where p is an odd prime, alpha is an element of Q is p-integral, <alpha >(p) is the least non-negative residue of a modulo p and (f) over cap (k) = Sigma(k)(j=0)(-1)(j) ((k)(j))f(j). This congruence implies several supercongruences of Rodriguez-Villegas. In this paper, we give a q-analogue, of this congruence and prove some symmetric q-congruences, which also confirm two conjectures of Guo and Zeng (2014). (C) 2019 Elsevier Inc. All rights reserved.