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arXiv · 2509.07556

Smoothed Shifted Convolutions of Generalised Divisor Functions

Cheuk Fung Lau
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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).

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Cheuk Fung Lau. 2025-09-09. Smoothed Shifted Convolutions of Generalised Divisor Functions. https://arxiv.org/abs/2509.07556

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