%0 Journal Article
%T A short proof of the multidimensional Szemer¨¦di theorem in the primes
%A Jacob Fox
%A Yufei Zhao
%J Mathematics
%D 2013
%I arXiv
%R 10.1353/ajm.2015.0028
%X Tao conjectured that every dense subset of $\mathcal{P}^d$, the $d$-tuples of primes, contains constellations of any given shape. This was very recently proved by Cook, Magyar, and Titichetrakun and independently by Tao and Ziegler. Here we give a simple proof using the Green-Tao theorem on linear equations in primes and the Furstenberg-Katznelson multidimensional Szemer\'edi theorem.
%U http://arxiv.org/abs/1307.4679v2