The Green-Tao theorem: an exposition

Abstract

The celebrated Green-Tao theorem states that the prime numbers contain arbitrarily long arithmetic progressions. We give an exposition of the proof, incorporating several simplifications that have been discovered since the original paper.

26 pages, 4 figures

References in corpus (7)

• The primes contain arbitrarily long polynomial progressions
• A quantitative improvement for Roth's theorem on arithmetic progressions
• Extremal results in sparse pseudorandom graphs
• A relative Szemerédi theorem
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• The regularity method for graphs with few 4-cycles
• Quantitative bounds in the inverse theorem for the Gowers $U^{s+1}$-norms over cyclic groups
• Szemerédi's theorem in the primes
• True complexity and iterated Cauchy--Schwarz
• Constellations in prime elements of number fields
• A transference principle for systems of linear equations, and applications to almost twin primes
• A counterexample to the Bollobás-Riordan conjectures on sparse graph limits
• Which graphs can be counted in $C_4$-free graphs?