Pointwise convergence of bilinear polynomial averages over the primes

Ben Krause, Hamed Mousavi, Terence Tao +1

We show that on a $\ddot{I}ƒ$-finite measure preserving system $X=(X,\hat{I}½,T)$, the non-conventional ergodic averages $${\mathbb{E}}_{n\in [N]}\hat{I}›(n)f(T^{n}x)g(T^{P(n)}x)$$ converge poi…