On the generalised Dirichlet divisor problem
In this talk we present new unconditional estimates on $\Delta_k(x)$, the remainder term of the generalised divisor function, for large $k$. By combining new estimates of exponential sums and Carlson's exponent, we show that $\Delta_k(x) \ll x^{1 - 1.224(k - 8.37)^{-2/3}}$ for $k\ge 30$ and $\Delta_k(x) \ll x^{1 - 3.699k^{-2/3}}$ for all sufficiently large fixed $k$. This is a joint work with Andrew Yang.
