Bounds on the gaps in the fractional parts of a linear form
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912247922556928 |
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| author | Kim, Seungki |
| author_facet | Kim, Seungki |
| contents | We provide bounds on the sizes of the gaps -- defined broadly -- in the set $\{k_1β_1 + \ldots + k_nβ_n \mbox{ (mod 1)} : k_i \in \mathbb Z \cap (0,Q^\frac{1}{n}]\}$ for generic $β_1, \ldots, β_n \in \mathbb R^m$ and all sufficiently large $Q$. We also introduce a related problem in Diophantine approximation, which we believe is of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02414 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bounds on the gaps in the fractional parts of a linear form Kim, Seungki Number Theory Dynamical Systems We provide bounds on the sizes of the gaps -- defined broadly -- in the set $\{k_1β_1 + \ldots + k_nβ_n \mbox{ (mod 1)} : k_i \in \mathbb Z \cap (0,Q^\frac{1}{n}]\}$ for generic $β_1, \ldots, β_n \in \mathbb R^m$ and all sufficiently large $Q$. We also introduce a related problem in Diophantine approximation, which we believe is of independent interest. |
| title | Bounds on the gaps in the fractional parts of a linear form |
| topic | Number Theory Dynamical Systems |
| url | https://arxiv.org/abs/2312.02414 |