An inverse theorem for the Gowers U s+1 [N] -norm

• Autores: Benjamin Green, Terence Tao, Tamar D. Ziegler
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 176, Nº 2, 2012, págs. 1231-1372
• Idioma: inglés
• DOI: 10.4007/annals.2012.176.2.11
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• Resumen

  • 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 ?f? U s+1 [N] =d , then there is a bounded-complexity s -step nilsequence F(g(n)G) that correlates with f , where the bounds on the complexity and correlation depend only on s and d . From previous results, this conjecture implies the Hardy-Littlewood prime tuples conjecture for any linear system of finite complexity.