Multiple recurrence and popular differences for polynomial patterns in rings of integers
DOI10.1017/s030500412300049xarXiv2107.07626OpenAlexW4387257886MaRDI QIDQ6198121
Vitaly Bergelson, Ethan M. Ackelsberg
Publication date: 20 February 2024
Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2107.07626
ergodic averagesWeyl's equidistribution theoremFurstenberg's correspondence principlepolynomial patterns
Ergodic theorems, spectral theory, Markov operators (37A30) General groups of measure-preserving transformations and dynamical systems (37A15) Relations between ergodic theory and number theory (37A44)
Cites Work
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- Polynomial averages converge to the product of integrals
- Multiple recurrence and convergence results associated to \(\mathbb F_P^\omega\)-actions
- Complexities of finite families of polynomials, Weyl systems, and constructions in combinatorial number theory
- Intersective polynomials and the polynomial Szemerédi theorem
- An ergodic Szemerédi theorem for IP-systems and combinatorial theory
- On density, translates, and pairwise sums of integers
- Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
- Multiple recurrence and nilsequences (with an appendix by Imre Ruzsa)
- Finite sums from sequences within cells of a partition of N
- \(\mathrm{IP}_r^\ast\)-recurrence and nilsystems
- An ergodic correspondence principle, invariant means and applications
- Polynomial ergodic averages for certain countable ring actions
- Nonconventional ergodic averages and nilmanifolds
- A Szemerédi-type regularity lemma in abelian groups, with applications
- Popular differences for right isosceles triangles
- Polynomial multiple recurrence over rings of integers
- An arithmetic regularity lemma, associated counting lemma, and applications
- Universal characteristic factors and Furstenberg averages
- Multiple ergodic averages for three polynomials and applications
- An ergodic IP polynomial Szemerédi theorem
- Sets of large values of correlation functions for polynomial cubic configurations
- Pointwise convergence of ergodic averages for polynomial actions of $\mathbb{Z}^{d}$ by translations on a nilmanifold
- Multiple recurrence and large intersections for abelian group actions
- Khintchine-type recurrence for 3-point configurations
- Nilsequences, null-sequences, and multiple correlation sequences
- ERGODIC AVERAGES FOR INDEPENDENT POLYNOMIALS AND APPLICATIONS
- Polynomial extensions of van der Waerden’s and Szemerédi’s theorems
- Popular differences for matrix patterns
- Multiple ergodic averages in abelian groups and Khintchine type recurrence
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