Smoothed Shifted Convolutions of Generalised Divisor Functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912578384429056 |
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| author | Lau, Cheuk Fung |
| author_facet | Lau, Cheuk Fung |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07556 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smoothed Shifted Convolutions of Generalised Divisor Functions Lau, Cheuk Fung Number Theory 11N37 (Primary) 11N75 (Secondary) 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). |
| title | Smoothed Shifted Convolutions of Generalised Divisor Functions |
| topic | Number Theory 11N37 (Primary) 11N75 (Secondary) |
| url | https://arxiv.org/abs/2509.07556 |