Multiple ergodic averages for three polynomials and applications

DOI10.1090/S0002-9947-08-04591-1zbMath1158.37006arXivmath/0606567OpenAlexW1973175673MaRDI QIDQ3533839

Nikos Frantzikinakis

Publication date: 24 October 2008

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

Full work available at URL: https://arxiv.org/abs/math/0606567

zbMATH Keywords

characteristic factormultiple recurrencemultiple ergodic averagespolynomial Szemerédi

Mathematics Subject Classification ID

Related Items (29)

On several notions of complexity of polynomial progressions ⋮ Khintchine-type recurrence for 3-point configurations ⋮ Some open problems on multiple ergodic averages ⋮ A Hardy field extension of Szemerédi's theorem ⋮ Multiple ergodic averages for flows and an application ⋮ Equidistribution of sparse sequences on nilmanifolds ⋮ Lower bound in the Roth theorem for amenable groups ⋮ Down the large rabbit hole ⋮ Multiple recurrence and convergence results associated to \(\mathbb F_P^\omega\)-actions ⋮ Multiple correlation sequences and nilsequences ⋮ Nilsequences and multiple correlations along subsequences ⋮ Multiple recurrence and convergence for Hardy sequences of polynomial growth ⋮ Host–Kra theory for -systems and multiple recurrence ⋮ Multiple recurrence and large intersections for abelian group actions ⋮ Juxtaposing combinatorial and ergodic properties of large sets of integers ⋮ Multiple recurrence and popular differences for polynomial patterns in rings of integers ⋮ Complexities of finite families of polynomials, Weyl systems, and constructions in combinatorial number theory ⋮ Optimal lower bounds for multiple recurrence ⋮ Intersective polynomials and the polynomial Szemerédi theorem ⋮ Orbit of the diagonal in the power of a nilmanifold ⋮ Multiple recurrence for two commuting transformations ⋮ True complexity of polynomial progressions in finite fields ⋮ Complexity of nilsystems and systems lacking nilfactors ⋮ Nil Bohr\(_0\)-sets and polynomial recurrence ⋮ Properties of multicorrelation sequences and large returns under some ergodicity assumptions ⋮ Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics ⋮ Multiple recurrence for non-commuting transformations along rationally independent polynomials ⋮ A spectral refinement of the Bergelson–Host–Kra decomposition and new multiple ergodic theorems ⋮ Multiple ergodic averages in abelian groups and Khintchine type recurrence

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