On some new infinite q -products and their vanishing coefficients

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