2000 character limit reached
A short proof of the multidimensional Szemerédi theorem in the primes (1307.4679v2)
Published 17 Jul 2013 in math.NT and math.CO
Abstract: 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.
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.