Evaluation of the convolution sums al+bm=n lσ(l) σ(m) with ab ≤ 9

Abstract

The generating functions of divisor functions are quasimodular forms of weight 2 and their products belong to a space of quasimodular forms of higher weight. In this article, we evaluate the convolution sumsal+bm=nlσ(l)σ(m) sumal+bm=n σ(l)σ(m) for all positive integers a, b and n with ab ≤ 9 and gcd(a, b) = 1. © 2017 Park.