Arbitrarily slow decay in the logarithmically averaged Sarnak conjecture
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917690136854528 |
|---|---|
| author | Algom, Amir Wang, Zhiren |
| author_facet | Algom, Amir Wang, Zhiren |
| contents | In 2017 Tao proposed a variant Sarnak's Möbius disjointness conjecture with logarithmic averaging: For any zero entropy dynamical system $(X,T)$, $\frac{1}{\log N} \sum_{n=1} ^N \frac{f(T^n x) μ(n)}{n}= o(1)$ for every $f\in \mathcal{C}(X)$ and every $x\in X$. We construct examples showing that this $o(1)$ can go to zero arbitrarily slowly. Nonetheless, all of our examples satisfy the conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06956 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arbitrarily slow decay in the logarithmically averaged Sarnak conjecture Algom, Amir Wang, Zhiren Dynamical Systems Number Theory In 2017 Tao proposed a variant Sarnak's Möbius disjointness conjecture with logarithmic averaging: For any zero entropy dynamical system $(X,T)$, $\frac{1}{\log N} \sum_{n=1} ^N \frac{f(T^n x) μ(n)}{n}= o(1)$ for every $f\in \mathcal{C}(X)$ and every $x\in X$. We construct examples showing that this $o(1)$ can go to zero arbitrarily slowly. Nonetheless, all of our examples satisfy the conjecture. |
| title | Arbitrarily slow decay in the logarithmically averaged Sarnak conjecture |
| topic | Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2406.06956 |