Average behavior of the triple divisor function over values of quadratic form (Q2038964)

Let \(d_3(n)\) denote the number of representations of \(n\) as the product of \(3\) natural numbers. The authors prove asymptotic formulas for this triple divisor function over values of a quadratic form \(n^2_1+\cdots+ n^2_l\) with \(l\ge 3\), i.e., for \(\sum_{1\le n_1,\dots, n_l\le \sqrt{x}} d_3(n^2_1+\cdots+ n^2_l)\). The proof uses the circle method.