On (not) computing the Mobius function using bounded depth circuits
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...
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| Format: | Journal article |
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2011
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| Summary: | 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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