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An inverse theorem for the Gowers U^{s+1}[N]-norm

Abstract:

We prove the inverse conjecture for the Gowers U^{s+1}[N]-norm for all s >= 3; this is new for s > 3, and the cases s<3 have also been previously established. More precisely, we establish that if f : [N] -> [-1,1] is a function with || f ||_{U^{s+1}[N]} > \delta then there is a bounded-complexity s-step nilsequence F(g(n)\Gamma) which correlates with f, where the bounds on the complexity and correlation depend only on s and \delta. From previous results, this conjecture implies...

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Publication date:
2010-09-21
URN:
uuid:2f2f71fc-43a9-4945-aec6-3756cab3d84d
Source identifiers:
398465
Local pid:
pubs:398465
Keywords:

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