Iterated differences sets, Diophantine approximations and applications

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:184

Article

Bergelson, Vitaly¹  Zelada, Rigoberto¹ 

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

关键词: Ramsey theory;    Diophantine approximations;    Ergodic theory;    Ultrafilters;   

DOI  :  10.1016/j.jcta.2021.105520

来源: Elsevier

【 摘 要 】

Let v be an odd real polynomial (i.e. a polynomial of the form Sigma(l)(j=1) a(j)x(2j-1)). We utilize sets of iterated differences to establish new results about sets of the form R(v, epsilon) = {n is an element of N vertical bar parallel to v(n) parallel to < epsilon} where parallel to.parallel to denotes the distance to the closest integer. We then apply the new Diophantineresults to obtain applications to ergodic theory and combinatorics. In particular, we obtain a new characterization of weakly mixing systems as well as a new variant of Furstenberg-Sarkozy theorem. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free