On the Fourier-Walsh Spectrum on the Moebius Function

Jean Bourgain

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arXiv · 1112.1423

On the Fourier-Walsh Spectrum on the Moebius Function

Jean Bourgain

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Abstract

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

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Jean Bourgain. 2011-12-06. On the Fourier-Walsh Spectrum on the Moebius Function. https://arxiv.org/abs/1112.1423

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