A structure theorem for level sets of multiplicative functions and applications

  title={A structure theorem for level sets of multiplicative functions and applications},
  author={Vitaly Bergelson and Joanna Kułaga-Przymus and Mariusz Lema'nczyk and Florian Karl Richter},
  journal={arXiv: Number Theory},
Given a level set $E$ of an arbitrary multiplicative function $f$, we establish, by building on the fundamental work of Frantzikinakis and Host [13,14], a structure theorem which gives a decomposition of $\mathbb{1}_E$ into an almost periodic and a pseudo-random parts. Using this structure theorem together with the technique developed by the authors in [3], we obtain the following result pertaining to polynomial multiple recurrence. Let $E=\{n_1<n_2<\ldots\}$ be a level set of an arbitrary… 
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