A multi-dimensional Szemerédi theorem for the primes via a correspondence principle
A multi-dimensional Szemerédi theorem for the primes via a correspondence principle
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基于对应原理的素数多维 Szemerédi 定理
DOI：
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发表时间：
2013
影响因子：
1
通讯作者：
T. Ziegler
中科院分区：
文献类型：
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作者：
T. Tao;T. Ziegler
我们在素数P：= {2，3，5，.}中建立了一个版本的Furstenberg-Katznelson多维Szemerédi定理，粗略地说，它断言Pd的任何稠密子集包含任何给定有理形状的有限星座。我们的论点是基于一个加权版本的Furstenberg对应原理，相对于一个重量服从一个无限数量的伪随机（或“线性形式”）的条件，结合主要成果的一系列文件的绿色和作者建立这样一个无限数量的伪随机条件的重量与素数。库克、马扎尔和提提切特拉昆，以及最近福克斯和赵，用一种相当不同的方法，同时得到了同样的结果。
We establish a version of the Furstenberg-Katznelson multi-dimensional Szemerédi theorem in the primes P:= {2, 3, 5, …}, which roughly speaking asserts that any dense subset of Pd contains finite constellations of any given rational shape. Our arguments are based on a weighted version of the Furstenberg correspondence principle, relative to a weight which obeys an infinite number of pseudorandomness (or “linear forms”) conditions, combined with the main results of a series of papers by Green and the authors which establish such an infinite number of pseudorandomness conditions for a weight associated with the primes. The same result, by a rather different method, has been simultaneously established by Cook, Magyar and Titichetrakun and more recently by Fox and Zhao.