Treffer: Vanishing coefficients of some new infinite q-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 (qr,qpk−r; qpk) ∞2(qs,q2pk−s; q2pk) ∞2(qt,q2pk−t; q2pk) ∞, 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 ∑n=−∞∞α(n)qn := (±q2t,±q17k−2t; q17k) ∞2(±qt,±q34k−t; q34k) ∞2(q4t,q34k−4t; q34k) ∞, where gcd(t, 17) = 1, then α(17n + 5t) = 0 for all non-negative integers n. [ABSTRACT FROM AUTHOR]