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arXiv · 1803.06481

The density of visible points in the Ammann-Beenker point set

Gustav Hammarhjelm
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Abstract

The relative density of visible points of the integer lattice $\mathbb{Z}^d$ is known to be $1/\zeta(d)$ for $d\geq 2$, where $\zeta$ is Riemann's zeta function. In this paper we prove that the relative density of visible points in the Ammann-Beenker point set is given by $2(\sqrt{2}-1)/\zeta_K(2)$, where $\zeta_K$ is Dedekind's zeta function over $K=\mathbb{Q}(\sqrt{2})$.

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Gustav Hammarhjelm. 2018-03-17. The density of visible points in the Ammann-Beenker point set. https://arxiv.org/abs/1803.06481

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