My aim is to understand Green-Tao theorem and all the related works. There is a question about understanding Green-Tao theorem but I seek for more broad references including the theorem and all other works.
Prerequisites to understand Green-Tao Theorem?
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number-theory
reference-request
prime-numbers
arithmetic-progressions
1 Answers
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Understand Szemeredi's relative theorem, the principle of transference, the norms of gowers and some results of analytical number theory. The W trick is fundamental
Primes in tuples I http://annals.math.princeton.edu/wp-content/uploads/annals-v170-n2-p10-p.pdf
A new proof of szemeredi theorem https://pdfs.semanticscholar.org/8861/7c3db354a943a9a6e2515d82797b6662f2c5.pdf
A quantitative ergodic theory proof of Szemerédi's theorem. https://arxiv.org/abs/math/0405251
THE ERGODIC AND COMBINATORIAL APPROACHES TO SZEMEREDI’S THEOREM https://arxiv.org/pdf/math/0604456.pdf
The primes contain arbitrarily long arithmetic progressions https://arxiv.org/abs/math/0404188
there is an extension of this theorem is for the Chen Primes and the prime numbers of the form $x ^ 2 + y^ 2 + 1$. They are the ones I know
Sun, Yu-Chen; Pan, Hao (2017). "The Green-Tao theorem for primes of the form $x^2+y^2+1$ https://arxiv.org/pdf/1708.08629.pdf
The Chen primes contain arbitrarily long arithmetic progressions. B Zhou 2009