An inverse theorem for the uniformity seminorms associated with the action of \(\mathbb F_p^\infty\)

DOI10.1007/s00039-010-0051-1zbMath1189.37007arXiv0901.2602OpenAlexW3124591719WikidataQ61645418 ScholiaQ61645418MaRDI QIDQ2379372

Tamar Ziegler, Terence C. Tao, Vitaly Bergelson

Publication date: 19 March 2010

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.2602

zbMATH Keywords

characteristic factorsGowers uniformity normspolynomials over finite fields.

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items

Approximately symmetric forms far from being exactly symmetric, Non-classical polynomials and the inverse theorem, Khintchine-type recurrence for 3-point configurations, Large values of the Gowers-Host-Kra seminorms, Regularity and inverse theorems for uniformity norms on compact abelian groups and nilmanifolds, Equivalence of polynomial conjectures in additive combinatorics, Approximate cohomology, Testing Linear-Invariant Properties, Multiple recurrence and convergence results associated to \(\mathbb F_P^\omega\)-actions, On higher-order Fourier analysis in characteristic p, Inverse theorem for certain directional Gowers uniformity norms, An uncountable Moore–Schmidt theorem, Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits, Host–Kra theory for -systems and multiple recurrence, Multiple recurrence and large intersections for abelian group actions, Partition and analytic rank are equivalent over large fields, Linear forms and higher-degree uniformity for functions on \(\mathbb F^n_p\), The inverse conjecture for the Gowers norm over finite fields in low characteristic, Properties of high rank subvarieties of affine spaces, An inverse theorem for the Gowers \(U^{s+1}[N\)-norm], Higher-order Fourier analysis of \(\mathbb F_p^n\) and the complexity of systems of linear forms, Polynomial functions as splines, Finite field models in arithmetic combinatorics -- ten years on, General systems of linear forms: equidistribution and true complexity, AN INVERSE THEOREM FOR THE GOWERSU⁴-NORM, On uniformity of q‐multiplicative sequences, Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors, Linear forms and quadratic uniformity for functions on \(\mathbb{Z}_{N}\), Multiple ergodic averages in abelian groups and Khintchine type recurrence, Pleasant extensions retaining algebraic structure. II

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