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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.21444 |
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| _version_ | 1866912789005598720 |
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| author | Haynes, Alan Lutsko, Christopher |
| author_facet | Haynes, Alan Lutsko, Christopher |
| contents | Let $B_R$ denote the closed Euclidean ball of radius $R$ in the plane. In this paper we prove that, if $V$ is the set of vertices of any unit length rhombic Penrose tiling then, for $R\ge 2$, \[\#(V\cap B_R)=πC_P R^2 + O(R^{2/3}(\log R)^{2/3}),\] where $C_P\approx 1.231$ is a constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21444 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Gauss circle problem for Penrose tilings Haynes, Alan Lutsko, Christopher Number Theory 11P21, 52C23, 11D45 Let $B_R$ denote the closed Euclidean ball of radius $R$ in the plane. In this paper we prove that, if $V$ is the set of vertices of any unit length rhombic Penrose tiling then, for $R\ge 2$, \[\#(V\cap B_R)=πC_P R^2 + O(R^{2/3}(\log R)^{2/3}),\] where $C_P\approx 1.231$ is a constant. |
| title | The Gauss circle problem for Penrose tilings |
| topic | Number Theory 11P21, 52C23, 11D45 |
| url | https://arxiv.org/abs/2512.21444 |