MULTIPLE RECURRENCE AND CONVERGENCE ALONG THE PRIMES

被引：23

作者：

Wooley, Trevor D. ^{[1
]}

Ziegler, Tamar D. ^{[2
]}

机构：

[1] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England

[2] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

来源：

AMERICAN JOURNAL OF MATHEMATICS | 2012年 / 134卷 / 06期

关键词：

DIFFERENCE SETS; ERGODIC AVERAGES; SEQUENCES; THEOREM; POLYNOMIALS; NILSEQUENCES; VARIABLES; NUMBERS;

D O I：

10.1353/ajm.2012.0048

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let E subset of Z be a set of positive upper density. Suppose that P-1, P-2, ... , P-k is an element of Z[X] are polynomials having zero constant terms. We show that the set E boolean AND (E - p(1)(p - 1)) boolean AND ... (E - P-k(P - 1)) is non-empty for some prime number p. Furthermore, we prove convergence in L-2 of polynomial multiple averages along the primes.

引用

页码：1705 / 1732

页数：28

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