English

On the Fourier-Walsh Spectrum on the Moebius Function

Number Theory 2011-12-08 v1

Abstract

We study the Fourier-Walsh spectrum {μ^(S);S{1,...,n}}\{\hat\mu (S); S\subset\{1, ..., n\}\} of the Moebius function μ\mu restricted to {0,1,2,...,2n1}{0,1}n\{0, 1, 2, ..., 2^n-1\}\simeq \{0, 1\}^n and prove that it is not captued by levels \{\hat\mu (S)| \, |S|< n^{\frac 23-\epsion}\}. An application to correlation with monotone Boelean functions is given.

Cite

@article{arxiv.1112.1423,
  title  = {On the Fourier-Walsh Spectrum on the Moebius Function},
  author = {Jean Bourgain},
  journal= {arXiv preprint arXiv:1112.1423},
  year   = {2011}
}
R2 v1 2026-06-21T19:47:30.379Z