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 sums ∑al+bm=nlσ(l)σ(m)$$\begin{array}{} \displaystyle\sum\limits_{al+bm=n}\,l\sigma(l)\sigma(m) \end{array} $$

Keywords

• divisor function
• convolution sum
• quasimodular form
• 11a25
• 11f11
• 11f20