Higher order divisor functions over values of mixed powers

Chenhao Du, Qingfeng Sun

Let $\ddot{I}{„}_k(n)$ be the $k$-th divisor function. In this paper, we derive an asymptotic formula for the sum $$ \sum_{1\leq n_1,n_2, \dots, n_{\ell}\leq X^{\frac{1}{r}} \atop 1\leq n_{…