One-dimensional quasi-uniform Kronecker sequences
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913402988789760 |
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| author | Goda, Takashi |
| author_facet | Goda, Takashi |
| contents | In this short note, we prove that the one-dimensional Kronecker sequence $iα\bmod 1, i=0,1,2,\ldots,$ is quasi-uniform if and only if $α$ is a badly approximable number. Our elementary proof relies on a result on the three-gap theorem for Kronecker sequences due to Halton (1965). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16352 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | One-dimensional quasi-uniform Kronecker sequences Goda, Takashi Number Theory In this short note, we prove that the one-dimensional Kronecker sequence $iα\bmod 1, i=0,1,2,\ldots,$ is quasi-uniform if and only if $α$ is a badly approximable number. Our elementary proof relies on a result on the three-gap theorem for Kronecker sequences due to Halton (1965). |
| title | One-dimensional quasi-uniform Kronecker sequences |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.16352 |