RESULTS OF HURWITZ TYPE FOR FIVE OR MORE SQUARES

Abstract

Let rk(n) denote the number of representations of n as a sum of k squares. We give many cases (for k = 5, 6, 7) in which the generating function n≥0 rk(an + b)q n is a simple infinite product. For instance, r7(24n + 23)q n = 49728 � (1 − q2n) 10 (1 − q3n) 3 (1 − qn) 6 n≥0 n≥