A short proof of the multidimensional Szemerédi theorem in the primes
Fox, Jacob · Zhao, Yufei
Original · EN
Tao conjectured that every dense subset of Pᵈ, 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 Szemerédi theorem.
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