- 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...
Expand abstract - 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:
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1469-509X
- ISSN:
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0017-0895
- URN:
-
uuid:b433c034-6ad3-40d1-a03d-6dfc04a815c2
- Source identifiers:
-
398468
- Local pid:
- pubs:398468
- Copyright date:
- 2009
- Notes:
-
49 pages, to appear in Glasgow J. Math. Fixed a problem with the file
(the paper appeared in duplicate)
Journal article
An inverse theorem for the Gowers U^4 norm
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