On the Gauss circle problem over smooth numbers
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918469268668416 |
|---|---|
| author | Gao, Peng |
| author_facet | Gao, Peng |
| contents | The Gauss circle problem concerns with the evaluation of $\sum_{n \leq x}r(n)$, where $r(n)$ denotes the number of representations of $n$ as sums of two squares and $x \geq 2$. Let $Ψ_G(x,y)$ denote the sum of $y$-smooth numbers below $x$ weighted by $r(n)$. In this paper, we evaluate $Ψ_G(x,y)$ asymptotically for certain ranges of $x \geq y \geq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23918 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Gauss circle problem over smooth numbers Gao, Peng Number Theory The Gauss circle problem concerns with the evaluation of $\sum_{n \leq x}r(n)$, where $r(n)$ denotes the number of representations of $n$ as sums of two squares and $x \geq 2$. Let $Ψ_G(x,y)$ denote the sum of $y$-smooth numbers below $x$ weighted by $r(n)$. In this paper, we evaluate $Ψ_G(x,y)$ asymptotically for certain ranges of $x \geq y \geq 2$. |
| title | On the Gauss circle problem over smooth numbers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2604.23918 |