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

Abstract:

In this note we announce the proof of the inverse conjecture for the Gowers U^{s+1}[N]-norm for all s => 3; this is new for s => 4, the cases s = 1,2,3 having been previously established. More precisely we outline a proof (details of which will appear in a forthcoming paper) 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 c...

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Publication date:
2010-06-01
URN:
uuid:933d498d-4d38-4c67-93d2-883dcd7974bf
Source identifiers:
398463
Local pid:
pubs:398463
Keywords:

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