On the Lindel\"{o}f Hypothesis for the Riemann Zeta function

In order to well understand the behaviour of the Riemann zeta function inside the critical strip, we show; among other things, the Fourier expansion of the ζᵏ(s) (k ∈ N) in the half-plane s > 1/2 and we deduce a necessary and sufficient condition for the truth of the Lindel\"{o}f Hypothesis. We conclude with some remarks and discussions.