Möbius disjointness for nilsequences along short intervals
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- by Xiaoguang He and Zhiren Wang PDF
- Trans. Amer. Math. Soc. 374 (2021), 3881-3917 Request permission
Abstract:
For a nilmanifold $G/\Gamma$, a $1$-Lipschitz continuous function $F$ and the Möbius sequence $\mu (n)$, we prove a bound on the decay of the averaged short interval correlation \begin{equation*} \frac {1}{HN}\sum _{n\leq N}\Big |\sum _{h\leq H} \mu (n+h)F(g^{n+h}x)\Big | \end{equation*} as $H,N\to \infty$. The bound is uniform in $g\in G$, $x\in G/\Gamma$ and $F$.References
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Additional Information
- Xiaoguang He
- Affiliation: School of Mathematics, Sichuan University, Chengdu, Sichuan 610064, People’s Republic of China
- MR Author ID: 1182917
- ORCID: 0000-0003-2159-762X
- Email: hexiaoguangsdu@gmail.com
- Zhiren Wang
- Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
- MR Author ID: 947740
- Email: zhirenw@psu.edu
- Received by editor(s): April 25, 2019
- Received by editor(s) in revised form: March 10, 2020, and April 15, 2020
- Published electronically: March 24, 2021
- Additional Notes: The first author is thankful for the financial support (No. 201706220146) from the China Scholarship Council.
The second author was supported by NSF grants DMS-1501095 and DMS-1753042. - © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 3881-3917
- MSC (2020): Primary 37A44; Secondary 11A25
- DOI: https://doi.org/10.1090/tran/8176
- MathSciNet review: 4251216