Smoothed Shifted Convolutions of Generalised Divisor Functions

Cheuk Fung Lau

Smoothed Shifted Convolutions of Generalised Divisor Functions

Number Theory 2025-09-10 v1

Authors: Cheuk Fung Lau

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).

Keywords

asymptotic formula smoothed shifted convolution generalised divisor function power-saving error term multiplicative number theory

Cite

@article{arxiv.2509.07556,
  title  = {Smoothed Shifted Convolutions of Generalised Divisor Functions},
  author = {Cheuk Fung Lau},
  journal= {arXiv preprint arXiv:2509.07556},
  year   = {2025}
}

Comments

25 pages

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