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

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

2011-03-25

arxiv.org/abs/1103.4991v2

Mathematics

Number Theory

10 pages, to appear in Combinatorics, Probability and Computing

Scientific paper

Any function F : {1,...,N} -> {-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_{x < N} 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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