Smoothed Shifted Convolutions of Generalised Divisor Functions

Cheuk Fung Lau

Published: 2025/9/9

Abstract

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