On the Fourier-Walsh Spectrum on the Moebius Function

Details On the Fourier-Walsh Spectrum on the Moebius Function On the Fourier-Walsh Spectrum on the Moebius Function

2011-12-06

arxiv.org/abs/1112.1423v1

Mathematics

Number Theory

Scientific paper

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 not captued by levels \{\hat\mu (S)| \, |S|<
n^{\frac 23-\epsion}\}. An application to correlation with monotone Boelean
functions is given.

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