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arXiv · 1103.4991

On (not) computing the Mobius function using bounded depth circuits

Ben Green
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Abstract

Any function F : {0,...,N-1} -> {-1,1} such that F(x) can be computed from the binary digits of x using a bounded depth circuit is orthogonal to the Mobius function mu in the sense that E_{0 <= x <= N-1} mu(x)F(x) = o(1). The proof combines a result of Linial, Mansour and Nisan with techniques of Katai and Harman-Katai, used in their work on finding primes with specified digits.

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Ben Green. 2012-06-01. On (not) computing the Mobius function using bounded depth circuits. https://arxiv.org/abs/1103.4991

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