Vanishing coefficients of some new infinite <i>q</i> -products

In this paper, we prove several vanishing coefficients in arithmetic progressions modulo 11, 13 and 17 by using elementary q-series manipulations and the Jacobi triple product identity for a new class of infinite q-products, namely [Formula: see text] where k is any positive integer, p is prime and r, s and t are integers that are relatively prime to p. For instance, we prove that for any positive integer k, if [Formula: see text] where [Formula: see text], then [Formula: see text] for all non-negative integers n.