Pointwise convergence of polynomial multiple ergodic averages along the primes

Mariusz Mirek, Renhui Wan, James Wright

We establish pointwise almost everywhere convergence for the polynomial multilinear ergodic averages $$\frac{1}{N} \sum_{n=1}^N \La(n) f_1(T^{P_1(n)} x)\cdots f_k(T^{P_k(n)} x)$$ a…