On the generalised Dirichlet divisor problem

We improve unconditional estimates on ${\mathrm{\Delta }}_k(x)$, the remainder term of the generalised divisor function, for large $k$. In particular, we show that ${\mathrm{\Delta }}_k(x)\ll x^{1-1.889k^{-2\mathrm{/}3}}$ for all sufficiently large fixed $k$.