On the Fourier-Walsh Spectrum on the Moebius Function

Jean Bourgain

We study the Fourier-Walsh spectrum $\{\hat{\mu }(S);S\subset \{1,...,n\}\}$ of the Moebius function $\mu$ restricted to $\{0,1,2,...,2^n-1\}\simeq \{0,1{\}}^n$ and prove that it is…