Erschienen:
Dept. of Mathematics, Princeton University, 2012
Erschienen in:Annals of Mathematics
Sprache:
Englisch
DOI:
10.4007/annals.2012.176.2.11
ISSN:
0003-486X
Entstehung:
Anmerkungen:
Beschreibung:
<p>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.</p>