Higher order Fourier analysis of multiplicative functions and applications

@article{Frantzikinakis2014HigherOF,
  title={Higher order Fourier analysis of multiplicative functions and applications},
  author={Nikos Frantzikinakis and Bernard Host},
  journal={arXiv: Number Theory},
  year={2014}
}
We prove a structure theorem for multiplicative functions which states that an arbitrary bounded multiplicative function can be decomposed into two terms, one that is approximately periodic and another that has small Gowers uniformity norm of an arbitrary degree. The proof uses tools from higher order Fourier analysis and some soft number theoretic input that comes in the form of an orthogonality criterion of K\'atai. We use variants of this structure theorem to derive applications of number… 
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