正密度集合中的无穷集合

IF 3.5 1区数学 Q1 MATHEMATICS Journal of the American Mathematical Society Pub Date : 2023-08-11 DOI:10.1090/jams/1030

Bryna Kra, Joel Moreira, Florian Richter, Donald Robertson

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引用次数: 0

摘要

受Erdős提出的问题的启发，我们证明了对于任意k∈N k\in \mathbb {N}，具有正上密度的任何集合A∧A\子集\mathbb {N}包含一个sumset b1 +⋯+B k B_1+\cdots +B_k，其中b1 B_1，…，B k∧N B_k\子集\mathbb {N}是无限的。我们的证明使用遍历理论并依赖于测度保持系统的结构结果。我们的技术是新的，即使对于以前已知的k=2 k=2的情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Infinite sumsets in sets with positive density

Motivated by questions asked by Erdős, we prove that any set A ⊂ N A\subset \mathbb {N} with positive upper density contains, for any k ∈ N k\in \mathbb {N} , a sumset B 1 + ⋯ + B k B_1+\cdots +B_k , where B 1 B_1 , …, B k ⊂ N B_k\subset \mathbb {N} are infinite. Our proof uses ergodic theory and relies on structural results for measure preserving systems. Our techniques are new, even for the previously known case of k = 2 k=2 .

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来源期刊

Journal of the American Mathematical Society 数学-数学

CiteScore

7.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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