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 $\zeta^k(s)$ ($k \in \mathbb{N}$) in the half-plane $\Re s > 1/2$ and we deduce a necessary and sufficient condition for the truth of the Lindel\"{o}f Hypothesis. We conclude with some remarks and discussions.