On the Fourier-Walsh Spectrum on the Moebius Function

2011/12/06 by Bourgain, Jean
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1112.1423

Abstract

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

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