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We prove quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm.
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B. Green and 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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B. Green and T. Tao, The primes contain arbitrarily long arithmetic progressions , Ann. of Math. (2) 167
2008
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B. Green and T. Tao, New bounds for Szemerédi’s theorem. II. A new bound for r 4 ( N ) r_{4}(N) , Analytic number theory, Cambridge Univ. Press, Cambridge, 2009, pp. 180–204
2009
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V. Bergelson, T. Tao, and T. Ziegler, An inverse theorem for the uniformity seminorms associated with the action of 𝔽 p ∞ \mathbb{F}^{\infty}_{p} , Geom. Funct. Anal. 19
2010
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W. T. Gowers and J. Wolf, The true complexity of a system of linear equations , Proc. Lond. Math. Soc. (3) 100
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B. Green and T. Tao, An arithmetic regularity lemma, an associated counting lemma, and applications , An irregular mind, Bolyai Soc. Math. Stud., vol. 21, János Bolyai Math. Soc., Budapest, 2010, pp. 261–334
T. Tao and T. Ziegler, The inverse conjecture for the Gowers norm over finite fields in low characteristic , Ann. Comb. 16
2012
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P. Candela, Notes on compact nilspaces , Discrete Anal. (2017), Paper No. 16, 57
2017
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P. Candela, Notes on nilspaces: algebraic aspects , Discrete Anal. (2017), Paper No. 15, 59
2017
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B. Green and T. Tao, New bounds for Szemerédi’s theorem, III: a polylogarithmic bound for r 4 ( N ) r_{4}(N) , Mathematika 63
2017
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T. Tao and T. Ziegler, Polynomial patterns in the primes , Forum Math. Pi 6
2018
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Y. Gutman, F. W. R. M. Manners, and P. P. Varjú, The structure theory of nilspaces II: Representation as nilmanifolds , Trans. Amer. Math. Soc. 371
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2010
Cited alongside, same era.
B. Green and T. Tao, Linear equations in primes , Ann. of Math. (2) 171
2010
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T. Tao and V. H. Vu, Additive combinatorics , Cambridge Studies in Advanced Mathematics, vol. 105, Cambridge University Press, Cambridge, 2010, Paperback edition [of MR2289012]
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 4 U^{4} -norm , Glasg. Math. J. 53
2011
Cited alongside, same era.
B. Green, T. Tao, and T. Ziegler, An inverse theorem for the Gowers U s + 1 [ N ] U^{s+1}[N] -norm , Electron. Res. Announc. Math. Sci. 18
2011
Cited alongside, same era.
B. Green and T. Tao, The Möbius function is strongly orthogonal to nilsequences , Ann. of Math. (2) 175
2012
Cited alongside, same era.
B. Green and T. Tao, The quantitative behaviour of polynomial orbits on nilmanifolds , Ann. of Math. (2) 175
2012
Cited alongside, same era.
2019
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Y. Gutman, F. W. R. M. Manners, and P. P. Varjú, The structure theory of nilspaces I , J. Anal. Math. 140
2020
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Y. Gutman, F. W. R. M. Manners, and P. P. Varjú, The structure theory of nilspaces III: Inverse limit representations and topological dynamics , Adv. Math. 365
2020
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T. Tao, Goursat and Furstenberg–Weiss type lemmas , 2021, blog post. https://terrytao.wordpress.com/2021/05/07/goursat-and-furstenberg-weiss-type-lemmas/
2021
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D. Altman, On a conjecture of Gowers and Wolf , Discrete Anal. (2022), Paper No. 10, 13
2022
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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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A. Jamneshan and 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), Paper No. 11, 48
2023
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T. Tao and J. Teräväinen, Quantitative bounds for Gowers uniformity of the Möbius and von Mangoldt functions , J. Eur. Math. Soc. (2023), 1–64
2023
Later among the works it cites.
A. Jamneshan, O. Shalom, and T. Tao, The structure of arbitrary Conze–Lesigne systems , Comm. Amer. Math. Soc. 4
2024
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