Reducing the Sarnak Conjecture to Toeplitz systems
In this paper, we show that for any sequence ${\bf a}=(a_n)_{n\in \Z}\in \{1,\ldots,k\}^\mathbb{Z}$ and any $\epsilon>0$, there exists a Toeplitz sequence ${\bf b}=(b_n)_{n\in \Z}\in \{1,\ldots,k\}^\mathbb{Z}$ such that the entropy $h({\bf b})\leq 2 h({\bf a})$ and $\lim_{N\to\infty}\frac{1}{2N+1...
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | In this paper, we show that for any sequence ${\bf a}=(a_n)_{n\in \Z}\in
\{1,\ldots,k\}^\mathbb{Z}$ and any $\epsilon>0$, there exists a Toeplitz
sequence ${\bf b}=(b_n)_{n\in \Z}\in \{1,\ldots,k\}^\mathbb{Z}$ such that the
entropy $h({\bf b})\leq 2 h({\bf a})$ and
$\lim_{N\to\infty}\frac{1}{2N+1}\sum_{n=-N}^N|a_n-b_n| |
|---|---|
| DOI: | 10.48550/arxiv.1908.07554 |