On (not) computing the Mobius function using bounded depth circuits
Number Theory
2012-06-04 v4
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.
Cite
@article{arxiv.1103.4991,
title = {On (not) computing the Mobius function using bounded depth circuits},
author = {Ben Green},
journal= {arXiv preprint arXiv:1103.4991},
year = {2012}
}
Comments
10 pages, to appear in Combinatorics, Probability and Computing. A few further small corrections