On the Sidon tails of $\left\{\lfloor x^n\rfloor\right\}$
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912898469593088 |
|---|---|
| author | Dutta, Sayan |
| author_facet | Dutta, Sayan |
| contents | We prove that the tail of the sets $$\mathbf S_x := \big\{\left\lfloor x^n\right\rfloor : n\in \mathbb N\big\}$$ are Sidon for almost all $x\in (1,2)$. Then we prove that for all $\varepsilon>0$, there exists $x\in (1,\, 1+\varepsilon)$ and $r\in (2-\varepsilon,\, 2)$ such that $\mathbf S_x$ and $\mathbf S_r$ do not have a Sidon tail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19807 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Sidon tails of $\left\{\lfloor x^n\rfloor\right\}$ Dutta, Sayan Number Theory Combinatorics General Topology We prove that the tail of the sets $$\mathbf S_x := \big\{\left\lfloor x^n\right\rfloor : n\in \mathbb N\big\}$$ are Sidon for almost all $x\in (1,2)$. Then we prove that for all $\varepsilon>0$, there exists $x\in (1,\, 1+\varepsilon)$ and $r\in (2-\varepsilon,\, 2)$ such that $\mathbf S_x$ and $\mathbf S_r$ do not have a Sidon tail. |
| title | On the Sidon tails of $\left\{\lfloor x^n\rfloor\right\}$ |
| topic | Number Theory Combinatorics General Topology |
| url | https://arxiv.org/abs/2601.19807 |