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Green, Ben; Tao, Terence; Ziegler, Tamar
Annals of mathematics, 09/2012, Letnik: 176, Številka: 2Journal Article
We prove the inverse conjecture for the Gowers U s+1 N-norm for all s ≥ 1; this is new for s ≥ 4. More precisely, we establish that if f : N → −1,1 is a function with ${\parallel \mathrm{f}\parallel }_{{\mathrm{U}}^{\mathrm{s}+1}\left\mathrm{N}\right}\ge \text{\hspace{0.17em}}\mathrm{\delta }$ , then there is a bounded-complexity s-step nilsequence F(g(n)Γ) that correlates with f, where the bounds on the complexity and correlation depend only on s and δ. From previous results, this conjecture implies the Hardy-Littlewood prime tuples conjecture for any linear system of finite complexity.
