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The Mobius function is strongly orthogonal to nilsequences

Abstract:

We show that the Mobius function mu(n) is strongly asymptotically orthogonal to any polynomial nilsequence n -> F(g(n)L). Here, G is a simply-connected nilpotent Lie group with a discrete and cocompact subgroup L (so G/L is a nilmanifold), g : Z -> G is a polynomial sequence and F: G/L -> R is a Lipschitz function. More precisely, we show that the inner product of mu(n) with F(g(n)L) over {1,...,N} is bounded by 1/log^A N, for all A > 0. In particular, this implies the Mobius and ...

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Publisher copy:
10.1103/PhysRevA.79.035801

Authors


Journal:
Physical Review A
Volume:
79
Issue:
3
Publication date:
2008-07-10
DOI:
EISSN:
1094-1622
ISSN:
1050-2947
URN:
uuid:0370dbba-8d10-4325-b2de-f79a7f02e0e1
Source identifiers:
398464
Local pid:
pubs:398464
Keywords:

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