Journal article
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...
Expand abstract
Actions
Access Document
- Publisher copy:
- 10.1017/S0017089510000546
Why is the content I wish to access not available via ORA?
Bibliographic data (the information relating to research outputs) and full-text items (e.g. articles, theses, reports, etc.) arrive in ORA from several different sources. Unfortunately we are not able to make available the full-text for every research output.
Please contact the ORA team (
) if you have queries regarding unavailable content OR if you are aware of a full-text copy we can make available.
) if you have queries regarding unavailable content OR if you are aware of a full-text copy we can make available.
Content may be unavailable for the following four reasons
-
Version unsuitable
-
We have not obtained a suitable full-text for a given research output. See this page for more information.
-
Recently completed
-
Sometimes content is held in ORA but is unavailable for a fixed period of time to comply with the policies and wishes of rights holders.
-
Permissions
-
All content made available in ORA should comply with relevant rights, such as copyright. See this page for more information.
-
Clearance
-
Some thesis volumes scanned as part of the digitisation scheme funded by Dr Leonard Polonsky are currently unavailable due to sensitive material or uncleared third-party copyright content. We are attempting to contact authors whose theses are affected.
Alternative access to the full-text
You may be able to access the full-text directly from the publisher's website using the 'Publisher Copy' link in the 'Links & Downloads' box from a research output's ORA record page. This method may require an institutional or individual subscription to the journal/resource.
Authors
Bibliographic Details
- 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
- Source identifiers:
-
398468
Item Description
Terms of use
- Copyright date:
- 2009
- Notes:
-
49 pages, to appear in Glasgow J. Math. Fixed a problem with the file
(the paper appeared in duplicate)
If you are the owner of this record, you can report an update to it here: Report update to this record