Note on a problem of Sárközy on multiplicative representation functions
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915531431346176 |
|---|---|
| author | Ding, Yuchen |
| author_facet | Ding, Yuchen |
| contents | Motivated by a 2001 problem of Sárközy, we classify all situations of the integers $b,c,e$ and $f$ satisfying \begin{align*} \limsup_{n\rightarrow\infty}|d(\mathcal{A},bn+c)-d(\mathcal{A},en+f)|=\infty \end{align*} for any infinite $\mathcal{A}\subset \mathbb{N}$, where $
d(\mathcal{A},m)=\#\{a\in \mathcal{A}:a|m\}. $ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Note on a problem of Sárközy on multiplicative representation functions Ding, Yuchen Number Theory Motivated by a 2001 problem of Sárközy, we classify all situations of the integers $b,c,e$ and $f$ satisfying \begin{align*} \limsup_{n\rightarrow\infty}|d(\mathcal{A},bn+c)-d(\mathcal{A},en+f)|=\infty \end{align*} for any infinite $\mathcal{A}\subset \mathbb{N}$, where $ d(\mathcal{A},m)=\#\{a\in \mathcal{A}:a|m\}. $ |
| title | Note on a problem of Sárközy on multiplicative representation functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.09545 |