A multi-dimensional Szemerédi theorem for the primes via a correspondence principle

Terence Tao*, Tamar Ziegler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

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.

Original languageAmerican English
Pages (from-to)203-228
Number of pages26
JournalIsrael Journal of Mathematics
Volume207
Issue number1
DOIs
StatePublished - 20 Apr 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015, Hebrew University of Jerusalem.

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