Explicit and Effective Estimates for the error term in the Generalised Divisor Problem

In this article, we obtain effective estimates for the error term ${\mathrm{\Delta }}_k(x)$ for all integers $k\ge 2$, and completely explicit estimates for integers $k\in [3,9]$. The explicit results improve the powers of $x$ appearing in the known explicit bounds for ${\mathrm{\Delta }}_k(x)$, and the effective bounds provide a method to derive such bounds for all integers $k\ge 3$.