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An inverse theorem for the Gowers U^4 norm

Abstract:

We prove the so-called inverse conjecture for the Gowers U^{s+1}-norm in the case s = 3 (the cases s < 3 being established in previous literature). That is, we establish that if f : [N] -> C is a function with |f(n)| <= 1 for all n and || f ||_{U^4} >= \delta then there is a bounded complexity 3-step nilsequence F(g(n)\Gamma) which correlates with f. The approach seems to generalise so as to prove the inverse conjecture for s >= 4 as well, and a longer paper will follow concern...

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Publisher copy:
10.1017/S0017089510000546

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Journal:
Glasgow Mathematical Journal (2011), 53 : pp 1-50
Volume:
53
Issue:
01
Pages:
1-50
Publication date:
2009-11-30
DOI:
EISSN:
1469-509X
ISSN:
0017-0895
URN:
uuid:b433c034-6ad3-40d1-a03d-6dfc04a815c2
Source identifiers:
398468
Local pid:
pubs:398468
Keywords:

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