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  • The inverse theorem for the U3 Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches
Title: The inverse theorem for the U3 Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches
We state and prove a quantitative inverse theorem for the Gowers uniformity norm U3(G) on an arbitrary finite abelian group G; the cases when G was of odd order or a vector space over F2 had previously been established by Green and the second author and by Samorodnitsky respectively by Fourier-analytic methods, which we also employ here. We also prove a qualitative version of this inverse theorem using a structure theorem of Host--Kra type for ergodic Zω-actions of order 2 on probability spaces established recently by Shalom and the authors.  more » « less
Award ID(s):
1764034
PAR ID:
10527579
Author(s) / Creator(s):
;
Publisher / Repository:
Alliance of Diamond Open Access Journals
Date Published:
Journal Name:
Discrete Analysis
ISSN:
2397-3129
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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