• Journal of applied mathematics & informatics
• /
• v.40 no.5_6
• /
• pp.813-830
• /
• 2022

The generating functions of the divisor function σ_s(n) = Σ_0<d|n d^s are quasimodular forms. In this paper, we find the basis of the space of quasimodular forms of weight 6 on Γ₀(10) consisting of Eisenstein series and η-quotients. Then we evaluate the convolution sum Σ_ak+bl+cm=n σ(k)σ(l)σ(m) with lcm(a, b, c) = 10 and Σ_al+bm=n lσ(l)σ(m) and Σ_al+bm=n σ₃(l)σ(m) with lcm(a, b) = 10.