The quantitative Beurling-Helson Theorem
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913016489967616 |
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| author | Sanders, Tom |
| author_facet | Sanders, Tom |
| contents | We show that for any $\varepsilon>0$ if $ϕ:\mathbb{T} \rightarrow \mathbb{T}$ is continuous and $\|\exp(-2πi z ϕ)\|_{A(\mathbb{T})} =O_{|z|\rightarrow \infty}(\log^{\frac{1}{8}-\varepsilon} |z|)$ then $ϕ(x)=wx+t$ for some $w \in\mathbb{Z}$ and $t \in \mathbb{T}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07324 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The quantitative Beurling-Helson Theorem Sanders, Tom Classical Analysis and ODEs We show that for any $\varepsilon>0$ if $ϕ:\mathbb{T} \rightarrow \mathbb{T}$ is continuous and $\|\exp(-2πi z ϕ)\|_{A(\mathbb{T})} =O_{|z|\rightarrow \infty}(\log^{\frac{1}{8}-\varepsilon} |z|)$ then $ϕ(x)=wx+t$ for some $w \in\mathbb{Z}$ and $t \in \mathbb{T}$. |
| title | The quantitative Beurling-Helson Theorem |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2604.07324 |