ERGODIC RECURRENCE AND BOUNDED GAPS BETWEEN PRIMES

被引：0

作者：

Pan, Hao ^{[1
]}

机构：

[1] Nanjing Univ Finance & Econ, Sch Appl Math, Nanjing 210046, Peoples R China

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2025年 / 378卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Ergodic recurrence; bounded gaps between primes; Kronecker factor; MULTIPLE RECURRENCE; AVERAGES;

D O I：

10.1090/tran/9299

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (X,B-X,mu,T) be a measure-preserving probability system with T is invertible. Suppose that A is an element of B-X with mu(A)>0 and & varepsilon; > 0. For any m >= 1, there exist infinitely many primes p0,p1,& mldr;,pm with p0<& ctdot;<pm such that mu(A boolean AND T(-(pi-1))A)>=mu(A)(2)-& varepsilon; for each 0 <= i <= m and p20-p0<C-m,C- A,C-is an element of where C-m,C- A,C-is an element of > 0 is a constant only depending on m, A and & varepsilon;.

引用

页码：1215 / 1234

页数：20

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