Means of powers of the zeta function

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.

• In papers and chapters (Titchmarsh and others) about the Dirichlet divisor problem – reuns Dec 6 '18 at 20:16
• Do you mean the equivalence? I am interested in the proofs of the estimate for $k=1, 2$. – Durac Dec 6 '18 at 20:27
• – reuns Dec 6 '18 at 20:40
• Thanks! Just a remark: this is the chapter of Titchmarsh titled 'Mean value theorems'. (You have answered my question, I am ready to accept.) – Durac Dec 6 '18 at 20:51