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Compact finite-rank nilspaces have become central in the nilspace approach to higher-order Fourier analysis, notably through their role in a general form of the inverse theorem for the Gowers norms.
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T. Tao, T. Ziegler, The inverse conjecture for the Gowers norm over finite fields via the correspondence principle , Anal. PDE 3
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Y. Gutman, F. Manners, P. Varjú, The structure theory of nilspaces III: Inverse limit representations and topological dynamics , Adv. Math. 365
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P. Candela, B. Szegedy, Regularity and inverse theorems for uniformity norms on compact abelian groups and nilmanifolds , J. Reine Angew. Math. 789
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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
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P. Candela, B. Szegedy, Nilspace factors for general uniformity seminorms, cubic exchangeability and limits , Mem. Amer. Math. Soc. 287
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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
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