Means of powers of the zeta function

Question

It is well known that the Lindel\"of Hypothesis is equivalent to the statement that $$\frac 1T\int_0^T|\zeta(1/2=it)|^{2k} =O(T^\epsilon)$$ for all positive integers $k$ and all positive real $\epsilon$, and these fact are known for $k=1, 2$. May I ask you for references to the proofs.