Minimal gap for higher dimensional sequences
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917633611268096 |
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| author | Bera, Tanmoy |
| author_facet | Bera, Tanmoy |
| contents | In this note, we extend the notion of minimal gaps to the higher dimensional sequences. We bound the minimal gap for $(\{\boldsymbol{a}_n\boldsymbolα\}),$ $(\{a_n\boldsymbolα\})$ and $(\{\boldsymbol{a}_n\cdot\boldsymbolα\})$ in terms of cardinality of the difference set of $a_n$ and $\boldsymbol{a}_n,$ where $a_n$ and $a_n^{(1)},\dots,a_n^{(d)}$ are sequences of distinct integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal gap for higher dimensional sequences Bera, Tanmoy Number Theory 11J13, 11J71, 11J83, 11K31 In this note, we extend the notion of minimal gaps to the higher dimensional sequences. We bound the minimal gap for $(\{\boldsymbol{a}_n\boldsymbolα\}),$ $(\{a_n\boldsymbolα\})$ and $(\{\boldsymbol{a}_n\cdot\boldsymbolα\})$ in terms of cardinality of the difference set of $a_n$ and $\boldsymbol{a}_n,$ where $a_n$ and $a_n^{(1)},\dots,a_n^{(d)}$ are sequences of distinct integers. |
| title | Minimal gap for higher dimensional sequences |
| topic | Number Theory 11J13, 11J71, 11J83, 11K31 |
| url | https://arxiv.org/abs/2404.05455 |