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arXiv · 1303.4137

Lattice points in rotated convex domains

Jingwei Guo
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Abstract

If $\mathcal{B}\subset \mathbb{R}^d$ ($d\geqslant 2$) is a compact convex domain with a smooth boundary of finite type, we prove that for almost every rotation $\theta\in SO(d)$ the remainder of the lattice point problem, $P_{\theta \mathcal{B}}(t)$, is of order $O_{\theta}(t^{d-2+2/(d+1)-\zeta_d})$ with a positive number $\zeta_d$. Furthermore we extend the estimate of the above type, in the planar case, to general compact convex domains.

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Jingwei Guo. 2013-03-18. Lattice points in rotated convex domains. https://arxiv.org/abs/1303.4137

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