Equidistribution of $\{p_n^2 \alpha \}$

Question

Let $p_n$ be the $n$th prime and $\alpha$ an irrational number. Vinogradov proved that the sequence $\{p_n \alpha \}$ is equidistributed. Is it known whether the sequence $\{p_n^2 \alpha \}$ is equidistributed?

I decided to crosspost to mathoverflow.

Answer 1

Yes, any polynomial in the primes with a non-constant irrational coefficient is equidistributed. See the mathoverflow answer.