Improving Roth's theorem in the primes
Résumé
Let A be a subset of the primes. Let δP (N) = |{n ∈ A : n ≤ N }|/ |{n prime : n ≤ N }| be the relative density of A in the primes. We prove that if
δP(N) ≥ C(log log log N)/(log log N)^{1/3} for N ≥ N0, where C and N0 are absolute constants, then A ∩ [1, N] contains a non-trivial three-term arithmetic progression. This improves on Green's result [4], which needs
δP(N) ≥ C'(log log log log log N/log log log log N)^{1/2}.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)
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