On the sum of ${\Delta }_k(n)$ in the Piltz divisor problem for $k=3$ and $k=4$

T. Makoto Minamide, Yoshio Tanigawa, Nigel Watt

Let ${\Delta }_k(x)$ be the error term in the classical asymptotic formula for the sum ${\sum }_{n\le x}{d}_k(n)$, where $d_k(n)$ is the number of ways $n$ can be written as a product of…