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arXiv · 1905.02864

M\"obius Disjointness for Nilsequences Along Short Intervals

Xiaoguang He·Zhiren Wang
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Abstract

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 $F$.

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Xiaoguang He, Zhiren Wang. 2019-05-08. M\"obius Disjointness for Nilsequences Along Short Intervals. https://arxiv.org/abs/1905.02864

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