  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.
