Estimates for smooth Weyl sums on minor arcs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910564620435456 |
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| author | Bruedern, Joerg Wooley, Trevor D. |
| author_facet | Bruedern, Joerg Wooley, Trevor D. |
| contents | We provide new estimates for smooth Weyl sums on minor arcs and explore their consequences for the distribution of the fractional parts of $αn^k$. In particular, when $k\ge 6$ and $ρ(k)$ is defined via the relation $ρ(k)^{-1}=k(\log k+8.02113)$, then for all large numbers $N$ there is an integer $n$ with $1\le n\le N$ for which $\| αn^k\|\le N^{-ρ(k)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06441 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Estimates for smooth Weyl sums on minor arcs Bruedern, Joerg Wooley, Trevor D. Number Theory 11L07, 11L15, 11P05 We provide new estimates for smooth Weyl sums on minor arcs and explore their consequences for the distribution of the fractional parts of $αn^k$. In particular, when $k\ge 6$ and $ρ(k)$ is defined via the relation $ρ(k)^{-1}=k(\log k+8.02113)$, then for all large numbers $N$ there is an integer $n$ with $1\le n\le N$ for which $\| αn^k\|\le N^{-ρ(k)}$. |
| title | Estimates for smooth Weyl sums on minor arcs |
| topic | Number Theory 11L07, 11L15, 11P05 |
| url | https://arxiv.org/abs/2408.06441 |