Complexities of finite families of polynomials, Weyl systems, and constructions in combinatorial number theory

DOI10.1007/s11854-008-0002-zzbMath1146.37007OpenAlexW1994747108MaRDI QIDQ926375

Vitaly Bergelson, Alexander Leibman, Emmanuel Lesigne

Publication date: 27 May 2008

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11854-008-0002-z

zbMATH Keywords

arithmetic progressionsmeasure-preserving transformationspolynomial Szemerédi theoremcomplexity of a system of polynomials

Mathematics Subject Classification ID

Related Items (11)

On several notions of complexity of polynomial progressions ⋮ Some open problems on multiple ergodic averages ⋮ Multiple ergodic averages for flows and an application ⋮ Juxtaposing combinatorial and ergodic properties of large sets of integers ⋮ Multiple recurrence and popular differences for polynomial patterns in rings of integers ⋮ Multiple ergodic averages for three polynomials and applications ⋮ Intersective polynomials and the polynomial Szemerédi theorem ⋮ Orbit of the diagonal in the power of a nilmanifold ⋮ Sets of large values of correlation functions for polynomial cubic configurations ⋮ True complexity of polynomial progressions in finite fields ⋮ Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors

Cites Work

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• Convergence of polynomial ergodic averages
• Polynomial averages converge to the product of integrals
• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Convergence of multiple ergodic averages along polynomials of several variables
• Nonconventional ergodic averages and nilmanifolds
• Universal characteristic factors and Furstenberg averages
• Multiple ergodic averages for three polynomials and applications
• Weakly mixing PET
• On sets of integers containing k elements in arithmetic progression
• Polynomial extensions of van der Waerden’s and Szemerédi’s theorems

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