Polynomial multiple recurrence over rings of integers

被引：2

作者：

Bergelson, Vitaly ^{[1
]}

Robertson, Donald ^{[1
]}

机构：

[1] Ohio State Univ, Dept Math, 231 W 18th Ave, Columbus, OH 43210 USA

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2016年 / 36卷

基金：

美国国家科学基金会;

关键词：

ERGODIC AVERAGES; TOPOLOGICAL DYNAMICS; SZEMEREDI; CONVERGENCE; SETS;

D O I：

10.1017/etds.2014.138

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We generalize the polynomial Szemeredi theorem to intersective polynomials over the ring of integers of an algebraic number field, by which we mean polynomials having a common root modulo every ideal. This leads to the existence of new polynomial configurations in positive-density subsets of Z(m) and strengthens and extends recent results of Bergelson, Leibman and Lesigne [Intersective polynomials and the polynomial Szemeredi theorem. Adv. Math. 219(1) (2008), 369-388] on polynomials over the integers.

引用

页码：1354 / 1378

页数：25

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