Multiple recurrence and convergence for certain averages along shifted primes

作者：Sun Wenbo^*

来源：Ergodic Theory and Dynamical Systems, 2015, 35(05): 1592-1609.

DOI：10.1017/etds.2014.6

We show that any subset A subset of N with positive upper Banach density contains the pattern {m, m +[n alpha], ... , m + k[n alpha]}, for some m is an element of N and n = p - 1 for some prime p, where alpha is an element of R\Q. Making use of the Furstenberg correspondence principle, we do this by proving an associated recurrence result in ergodic theory along the shifted primes. We also prove the convergence result for the associated averages along primes and indicate other applications of these methods.

• 出版日期2015-8
• 单位西北大学