Sums of the triple divisor function over values of a ternary quadratic form

Qingfeng Sun, Deyu Zhang

Let ${\tau }_3(n)$ be the triple divisor function which is the number of solutions of the equation $d_1{d}_2{d}_3=n$ in natural numbers. It is shown that $$ \sum_{1\leq n_1,n_2,n_3\leq \sqrt…