Publications

2024

Additive and geometric transversality of fractal sets in the integers

D. Glasscock; J. Moreira; F. K. Richter 

Journal Of The London Mathematical Society-Second Series. 2024-05-01. Vol. 109, num. 5, p. e12902. DOI : 10.1112/jlms.12902.

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Multiple ergodic averages along functions from a Hardy field: Convergence, recurrence and combinatorial applications

V. Bergelson; J. Moreira; F. K. Richter 

Advances In Mathematics. 2024-03-08. Vol. 443, p. 109597. DOI : 10.1016/j.aim.2024.109597.

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2023

Zero-one laws for eventually always hitting points in rapidly mixing systems

D. Kleinbock; I. Konstantoulas; F. K. Richter 

Mathematical Research Letters. 2023-01-01. Vol. 30, num. 3, p. 765–805. DOI : 10.4310/MRL.2023.v30.n3.a7.

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A combinatorial proof of a sumset conjecture of Furstenberg

D. Glasscock; J. Moreira; F. K. Richter; F. K. Richter 

Combinatorica. 2023-06-14. DOI : 10.1007/s00493-023-00008-9.

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2022

On Katznelson’s Question for skew-product systems

D. Glasscock; A. Koutsogiannis; F. K. Richter 

Bulletin of the American Mathematical Society. 2022. Vol. 59, p. 569-606. DOI : 10.1090/bull/1764.

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Dynamical generalizations of the prime number theorem and disjointness of additive and multiplicative semigroup actions

V. Bergelson; F. K. Richter 

Duke Mathematical Journal. 2022-10-15. Vol. 171, num. 15, p. 3133-3200. DOI : 10.1215/00127094-2022-0055.

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2021

Additive and geometric transversality of fractal sets in the integers

D. Glasscock; J. Moreira; F. K. Richter 

arXiv. 2021-07-20. 

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A decomposition of multicorrelation sequences for commuting transformations along primes

A. N. Le; J. Moreira; F. K. Richter 

Discrete Analysis. 2021-06-07.  p. 22056. DOI : 10.19086/da.22056.

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Structure of multicorrelation sequences with integer part polynomial iterates along primes

A. Koutsogiannis; A. Le; J. Moreira; F. K. Richter 

Proceedings of the American Mathematical Society. 2021. Vol. 149, num. 1, p. 209-216. DOI : 10.1090/proc/15185.

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A new elementary proof of the Prime Number Theorem

F. K. Richter 

Bulletin of the London Mathematical Society. 2021-10. Vol. 53, num. 5, p. 1365-1375. DOI : 10.1112/blms.12503.

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2020

A Structure Theorem for Level Sets of Multiplicative Functions and Applications

V. Bergelson; J. Kułaga-Przymus; M. Lemańczyk; F. K. Richter 

International Mathematics Research Notices. 2020-03-01. Vol. 2020, num. 5, p. 1300-1345. DOI : 10.1093/imrn/rny040.

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Single and multiple recurrence along non-polynomial sequences

V. Bergelson; J. Moreira; F. K. Richter 

Advances in Mathematics. 2020-07-15. Vol. 368, p. 107146. DOI : 10.1016/j.aim.2020.107146.

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Uniform distribution in nilmanifolds along functions from a Hardy field

F. K. Richter 

arXiv. 2020-06-02. 

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Zero-one laws for eventually always hitting points in in rapidly mixing systems

D. Kleinbock; I. Konstantoulas; F. K. Richter 

arXiv. 2020-12-02. 

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Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

V. Bergelson; J. Moreira; F. K. Richter 

arXiv. 2020-06-05. 

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2019

A spectral refinement of the Bergelson–Host–Kra decomposition and new multiple ergodic theorems

J. Moreira; F. K. Richter 

Ergodic Theory and Dynamical Systems. 2019-04. Vol. 39, num. 4, p. 1042-1070. DOI : 10.1017/etds.2017.61.

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Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

V. Bergelson; J. Kułaga-Przymus; M. Lemańczyk; F. K. Richter 

Ergodic Theory and Dynamical Systems. 2019-09. Vol. 39, num. 9, p. 2332-2383. DOI : 10.1017/etds.2017.130.

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A generalization of Kátai’s orthogonality criterion with applications

V. Bergelson; J. Kułaga-Przymus; M. Lemańczyk; F. K. Richter 

Discrete & Continuous Dynamical Systems. 2019. Vol. 39, num. 5, p. 2581. DOI : 10.3934/dcds.2019108.

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Multiplicative combinatorial properties of return time sets in minimal dynamical systems

D. Glasscock; A. Koutsogiannis; F. K. Richter 

Discrete & Continuous Dynamical Systems. 2019. Vol. 39, num. 10, p. 5891. DOI : 10.3934/dcds.2019258.

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A proof of a sumset conjecture of Erdős

J. Moreira; F. K. Richter; D. Robertson 

Annals of Mathematics. 2019. Vol. 189, num. 2, p. 605-652. DOI : 10.4007/annals.2019.189.2.4.

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2017

Revisiting the nilpotent polynomial Hales–Jewett theorem

J. H. Johnson; F. K. Richter 

Advances in Mathematics. 2017-12-01. Vol. 321, p. 269-286. DOI : 10.1016/j.aim.2017.09.033.

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On the Density of Coprime Tuples of the Form (n, ⌊f_1(n)⌋, …, ⌊f_k(n)⌋), Where f_1, …, f_k Are Functions from a Hardy Field

V. Bergelson; F. K. Richter 

Number Theory – Diophantine Problems, Uniform Distribution and Applications: Festschrift in Honour of Robert F. Tichy’s 60th Birthday; Cham: Springer International Publishing, 2017. p. 109-135.

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Disjointness for measurably distal group actions and applications

J. Moreira; F. K. Richter; D. Robertson 

Ergodic Theory and Dynamical Systems. 2017-08-06.  p. 1-28. DOI : 10.1017/etds.2022.19.

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2016

Large subsets of discrete hypersurfaces in Z^d contain arbitrarily many collinear points

J. Moreira; F. K. Richter 

European Journal of Combinatorics. 2016-05-01. Vol. 54, num. C, p. 163–176. DOI : 10.1016/j.ejc.2015.12.012.

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