Nilsystems and ergodic averages along primes

被引：2
作者：
Eisner, Tanja [1 ]
机构：
[1] Univ Leipzig, Inst Math, POB 100 920, D-04009 Leipzig, Germany
来源：
ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2020年 / 40卷 / 10期
关键词：
ergodic averages along primes; nilsystems; everywhere convergence; CIRCLE METHOD APPROACH; MULTIPLE RECURRENCE; THEOREM; CONVERGENCE; POLYNOMIALS; SEQUENCES; SZEMEREDI; UNIFORMITY; BEHAVIOR;
D O I：
10.1017/etds.2019.27
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A celebrated result by Bourgain and Wierdl states that ergodic averages along primes converge almost everywhere for L-p-functions, p > 1, with a polynomial version by Wierdl and Nair. Using an anti-correlation result for the von Mangoldt function due to Green and Tao, we observe everywhere convergence of such averages for nilsystems and continuous functions.
引用
收藏
页码：2769 / 2777
页数：9
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