-
A short proof of the multidimensional Szemerédi theorem in the primes
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 137, Number 4, August 2015
- pp. 1139-1145
- 10.1353/ajm.2015.0028
- Article
- Additional Information
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.