Functions tiling simultaneously with two arithmetic progressions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866914945094909952 |
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| author | Etkind, Mark Mordechai Lev, Nir |
| author_facet | Etkind, Mark Mordechai Lev, Nir |
| contents | We consider measurable functions $f$ on $\mathbb{R}$ that tile simultaneously by two arithmetic progressions $α\mathbb{Z}$ and $β\mathbb{Z}$ at respective tiling levels $p$ and $q$. We are interested in two main questions: what are the possible values of the tiling levels $p,q$, and what is the least possible measure of the support of $f$? We obtain sharp results which show that the answers depend on arithmetic properties of $α, β$ and $p,q$, and in particular, on whether the numbers $α, β$ are rationally independent or not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_16058 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Functions tiling simultaneously with two arithmetic progressions Etkind, Mark Mordechai Lev, Nir Classical Analysis and ODEs Combinatorics 05B45, 15B51 We consider measurable functions $f$ on $\mathbb{R}$ that tile simultaneously by two arithmetic progressions $α\mathbb{Z}$ and $β\mathbb{Z}$ at respective tiling levels $p$ and $q$. We are interested in two main questions: what are the possible values of the tiling levels $p,q$, and what is the least possible measure of the support of $f$? We obtain sharp results which show that the answers depend on arithmetic properties of $α, β$ and $p,q$, and in particular, on whether the numbers $α, β$ are rationally independent or not. |
| title | Functions tiling simultaneously with two arithmetic progressions |
| topic | Classical Analysis and ODEs Combinatorics 05B45, 15B51 |
| url | https://arxiv.org/abs/2211.16058 |