M\"{o}bius disjointness for a class of exponential functions

Weichen Gu Department of Mathematics, University of New Hampshire, Durham, NH 03824, USA --and--Academy of Mathematics and Systems Science, Chinese Academy of Sciences Fei Wei Yau Mathematical Sciences Center, Tsinghua University

Dynamical Systems Number Theory mathscidoc:2205.11013

The Quarterly Journal of Mathematics, 2022.3
A vast class of exponential functions are shown to be deterministic. This class includes functions whose exponents are polynomial-like or ``piece-wise'' close to polynomials after differentiation. Many of these functions are proved to be disjoint from the M\"obius function.
M\"obius function, disjointness, $k$-th difference
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@inproceedings{weichen2022m\"{o}bius,
  title={M\"{o}bius disjointness for a class of exponential functions},
  author={Weichen Gu, and Fei Wei},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517164703428668242},
  booktitle={The Quarterly Journal of Mathematics},
  year={2022},
}
Weichen Gu, and Fei Wei. M\"{o}bius disjointness for a class of exponential functions. 2022. In The Quarterly Journal of Mathematics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517164703428668242.
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