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The inverse theorem for the $U^3$ Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches
Discrete analysis (2023) Cet article a éte moissonné depuis la source Scholastica

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We state and prove a quantitative inverse theorem for the Gowers uniformity norm $U^3(G)$ on an arbitrary finite abelian group $G$; the cases when $G$ was of odd order or a vector space over ${\mathbf F}_2$ 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 ${\mathbf Z}^ω$-actions of order $2$ on probability spaces established recently by Shalom and the authors.
Publié le : 
@article{DAS_2023_a11,
     author = {Asgar Jamneshan and Terence Tao},
     title = {The inverse theorem for the $U^3$ {Gowers} uniformity norm on arbitrary finite abelian groups: {Fourier-analytic} and ergodic approaches},
     journal = {Discrete analysis},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2023_a11/}
}
TY  - JOUR
AU  - Asgar Jamneshan
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TI  - The inverse theorem for the $U^3$ Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches
JO  - Discrete analysis
PY  - 2023
UR  - http://geodesic.mathdoc.fr/item/DAS_2023_a11/
LA  - en
ID  - DAS_2023_a11
ER  - 
%0 Journal Article
%A Asgar Jamneshan
%A Terence Tao
%T The inverse theorem for the $U^3$ Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches
%J Discrete analysis
%D 2023
%U http://geodesic.mathdoc.fr/item/DAS_2023_a11/
%G en
%F DAS_2023_a11
Asgar Jamneshan; Terence Tao. The inverse theorem for the $U^3$ Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches. Discrete analysis (2023). http://geodesic.mathdoc.fr/item/DAS_2023_a11/