On higher-order Fourier analysis in characteristic p

DOI10.1017/etds.2022.119arXiv2109.15281OpenAlexW3203010451MaRDI QIDQ6068432

Diego Gonzalez-Sanchez, Pablo Candela, Balázs Szegedy

Publication date: 15 December 2023

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.15281

zbMATH Keywords

finite fieldsHost-Kra factorsGowers normsnilspaces

Mathematics Subject Classification ID

Finite nilpotent groups, (p)-groups (20D15) Class field theory; (p)-adic formal groups (11S31) Homogeneous flows (37A17) Relations between ergodic theory and number theory (37A44) Relations between ergodic theory and harmonic analysis (37A46)

Cites Work

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• The inverse conjecture for the Gowers norm over finite fields in low characteristic
• The inverse conjecture for the Gowers norm over finite fields via the correspondence principle
• Multiple recurrence and convergence results associated to \(\mathbb F_P^\omega\)-actions
• Higher order regionally proximal equivalence relations for general minimal group actions
• Strictly ergodic distal models and a new approach to the Host-Kra factors
• Regularity and inverse theorems for uniformity norms on compact abelian groups and nilmanifolds
• The structure theory of nilspaces. I
• The structure theory of nilspaces. III: Inverse limit representations and topological dynamics
• An inverse theorem for the uniformity seminorms associated with the action of \(\mathbb F_p^\infty\)
• Nonconventional ergodic averages and nilmanifolds
• Finite field models in arithmetic combinatorics -- ten years on
• A refinement of Cauchy-Schwarz complexity
• AN INVERSE THEOREM FOR THE GOWERSU⁴-NORM
• An arithmetic regularity lemma, associated counting lemma, and applications
• Parallelepipeds, nilpotent groups and Gowers norms
• Nilpotent Structures in Ergodic Theory
• The structure theory of Nilspaces II: Representation as nilmanifolds
• http://discreteanalysisjournal.com/article/2105-notes-on-nilspaces-algebraic-aspects
• Notes on compact nilspaces
• Good Bounds in Certain Systems of True Complexity One
• On nilspace systems and their morphisms
• Non-classical polynomials and the inverse theorem
• A bilinear version of Bogolyubov’s theorem
• AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM
• Metric automorphisms with quasi-discrete spectrum
• Multiple ergodic averages in abelian groups and Khintchine type recurrence
• An inverse theorem for the Gowers \(U^{s+1}[N\)-norm]
• A new proof of Szemerédi's theorem
• Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits
• Host–Kra theory for -systems and multiple recurrence

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