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

被引：130

作者：

Green, Ben ^{[1
]}

Tao, Terence ^{[2
]}

Ziegler, Tamar ^{[3
]}

机构：

[1] Ctr Math Sci, Cambridge, England

[2] Univ Calif Los Angeles, Los Angeles, CA USA

[3] Technion Israel Inst Technol, Haifa, Israel

来源：

ANNALS OF MATHEMATICS | 2012年 / 176卷 / 02期

关键词：

POLYNOMIAL-SEQUENCES; UNIFORM-DISTRIBUTION; MULTIPLE RECURRENCE; ERGODIC AVERAGES; CONVERGENCE; EQUATIONS; SZEMEREDI; BEHAVIOR; VALUES; PROOF;

D O I：

10.4007/annals.2012.176.2.11

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the inverse conjecture for the Gowers Us+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 to f parallel to(Us+1) ([N]) >= delta, then there is a bounded-complexity s-step nilsequence F(g(n)Gamma) that correlates with f, where the bounds on the complexity and correlation depend only on s and delta. From previous results, this conjecture implies the Hardy-Littlewood prime tuples conjecture for any linear system of finite complexity.

引用

页码：1231 / 1372

页数：142

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