Evaluation of the convolution sums ∑ak+bl+cm=nσ(k)σ(l)σ(m) with lcm(a,b,c) = 7,8 or 9

Abstract

It is known that the generating functions of divisor functions are quasimodular forms of weight (Formula presented.). Hence their product is a quasimodular form of higher weight. In this paper, we evaluate the convolution sums (Formula presented.) for all positive integers (Formula presented.) with (Formula presented.) or (Formula presented.) using theory of modular form. © 2018 World Scientific Publishing Company