Smoothed Shifted Convolutions of Generalised Divisor Functions

Abstract

We prove an asymptotic formula for the smoothed shifted convolution of the generalised divisor function $d_k(n)$ and the divisor function $d(n)$ for $k\ge 4$, with a power-saving error term whose exponent is independent of $k$. In particular, for sufficiently large $k$, this improves on the result of Topacogullari (2018).

25 pages