A generalization of Kátai's orthogonality criterion with applications

@article{Bergelson2019AGO,
  title={A generalization of K{\'a}tai's orthogonality criterion with applications},
  author={Vitaly Bergelson and Joanna Kułaga-Przymus and Mariusz Lema'nczyk and Florian Karl Richter},
  journal={Discrete \& Continuous Dynamical Systems - A},
  year={2019}
}
We study properties of arithmetic sets coming from multiplicative number theory and obtain applications in the theory of uniform distribution and ergodic theory. Our main theorem is a generalization of Katai's orthogonality criterion. Here is a special case of this theorem: Let $a\colon\mathbb{N}\to\mathbb{C}$ be a bounded sequence satisfying $$ \sum_{n\leq x} a(pn)\overline{a(qn)} = {\rm o}(x),~\text{for all distinct primes $p$ and $q$.} $$ Then for any multiplicative function $f$ and any $z… 
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