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In recent work, Jamneshan, Shalom and Tao proved an inverse theorem for the Gowers $U^{k+1}$-norm on finite abelian groups of fixed torsion $m$, where the final correlating harmonic is a polynomial phase function of degree at most $C(k,m)$.
W. T. Gowers, A new proof of Szemerédi’s theorem , Geom. Funct. Anal. 11
2001
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2002
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H. Kurzweil, B. Stellmacher, The Theory of Finite Groups. An introduction. Translated from the 1998 German original Universitext Springer-Verlag, New York, 2004. xii+387 pp
2004
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T. Tao, V. Vu, Additive combinatorics , Cambridge Stud. Adv. Math., 105 Cambridge University Press, Cambridge, 2006. xviii+512 pp
2006
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B. Green, T. Tao, An inverse theorem for the Gowers U 3 ( G ) U^{3}(G) -norm , Proc. Edinb. Math. Soc. (2) 51
2008
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2010
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W. T. Gowers, Decompositions, approximate structure, transference, and the Hahn-Banach theorem , Bull. Lond. Math. Soc. 42
2010
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B. Green, T. Tao, Linear equations in primes , Ann. of Math. (2) 171
2010
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2010
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T. Tao and T. Ziegler, The inverse conjecture for the Gowers norm over finite fields via the correspondence principle , Anal. PDE 3
2010
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B. Green, T. Tao and T. Ziegler, An inverse theorem for the Gowers U s + 1 [ N ] U^{s+1}[N] -norm , Ann. of Math. (2) 176
2012
Cited alongside, same era.
T. Tao and T. Ziegler, The inverse conjecture for the Gowers norm over finite fields in low characteristic , Ann. Comb. 16
2012
Cited alongside, same era.
J. Feng, A note on computing of positive integer powers for circulant matrices , Appl. Math. Comput. Appl. Math. Comput. 223
2013
Cited alongside, same era.
P. Candela, Notes on nilspaces: algebraic aspects , Discrete Anal. (2017), Paper No. 15, 59 pp
2017
Cited alongside, same era.
P. Candela, Notes on compact nilspaces , Discrete Anal. (2017), Paper No. 16, 57 pp
2017
Cited alongside, same era.
Y. Gutman, F. Manners, P. P. Varjú, The structure theory of nilspaces I , J. Anal. Math. 140
2020
Later among the works it cites.
Y. Gutman, F. Manners, P. P. Varjú, The structure theory of nilspaces III: Inverse limit representations and topological dynamics , Adv. Math. 365
2020
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2021
Later among the works it cites.
P. Candela and B. Szegedy, Regularity and inverse theorems for uniformity norms on compact abelian groups and nilmanifolds , J. Reine Angew. Math. 789
2022
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2017
Cited alongside, same era.
B. Host and B. Kra, Nilpotent structures in ergodic theory , Math. Surveys Monogr., 236 American Mathematical Society, Providence, RI, 2018. X+427 pp
2018
Cited alongside, same era.
2018
Cited alongside, same era.
Y. Gutman, F. Manners, P. P. Varjú, The structure theory of nilspaces II: Representation as nilmanifolds , Trans. Amer. Math. Soc. 371
2019
Cited alongside, same era.
P. Candela, D. González-Sánchez and B. Szegedy On nilspace systems and their morphisms , Ergodic Theory Dynam. Systems 40
2020
Cited alongside, same era.
2023
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P. Candela, D. González-Sánchez, B. Szegedy, On higher-order Fourier analysis in characteristic p p , Ergodic Theory Dynam. Systems 43
2023
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P. Candela and B. Szegedy, Nilspace factors for general uniformity seminorms, cubic exchangeability and limits , Mem. Amer. Math. Soc. 287
2023
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A. Jamneshan, T. Tao, The inverse theorem for the U 3 U^{3} Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches , Discrete Anal., 2023:11, 48 pp
2023
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