M\'obius Disjointness for Nilsequences Along Short Intervals
| Autor: | He, Xiaoguang, Wang, Zhiren |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | For a nilmanifold $G/\Gamma$, a $1$-Lipschitz continuous function $F$ and the M\"obius sequence $\mu(n)$, we prove a bound on the decay of the averaged short interval correlation $$\frac1{HN}\sum_{n\leq N}\Big|\sum_{h\leq H} \mu(n+h)F(g^{n+h}x)\Big|$$ as $H,N\to\infty$. The bound is uniform in $g\in G$, $x\in G/\Gamma$ and $F$. Comment: 35 pages |
| Databáze: | arXiv |
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