A bilinear version of Bogolyubov’s theorem

DOI10.1090/proc/15129zbMath1456.11014arXiv1712.00248OpenAlexW3026248260WikidataQ128340070 ScholiaQ128340070MaRDI QIDQ5119225

Luka Milićević, Timothy Gowers

Publication date: 3 September 2020

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.00248

zbMATH Keywords

Fourier analysissumsetsadditive combinatoricsbilinear setsBogolyubov-Ruzsa lemma

Mathematics Subject Classification ID

Inverse problems of additive number theory, including sumsets (11P70) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (7)

Approximately symmetric forms far from being exactly symmetric ⋮ Regularity and inverse theorems for uniformity norms on compact abelian groups and nilmanifolds ⋮ On higher-order Fourier analysis in characteristic p ⋮ Subsets of without L-shaped configurations ⋮ Partition and analytic rank are equivalent over large fields ⋮ Properties of high rank subvarieties of affine spaces ⋮ A note on extensions of multilinear maps defined on multilinear varieties

Cites Work

• Generalized arithmetical progressions and sumsets
• A statistical theorem of set addition
• A bilinear Bogolyubov theorem
• On the Bogolyubov-Ruzsa lemma
• A note on the bilinear Bogolyubov theorem: Transverse and bilinear sets
• A bilinear Bogolyubov-Ruzsa lemma with poly-logarithmic bounds
• LINEAR AND QUADRATIC UNIFORMITY OF THE MÖBIUS FUNCTION OVER
• AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM
• A new proof of Szemerédi's theorem
• Unnamed Item

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