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arXiv · 2604.23918

On the Gauss circle problem over smooth numbers

Peng Gao
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Abstract

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 $x \geq y \geq 2$.

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Peng Gao. 2026-04-27. On the Gauss circle problem over smooth numbers. https://arxiv.org/abs/2604.23918

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