Lindel\" of hypothesis and the order of the mean-value of $\mathrm{\mid }\zeta (s){\mathrm{\mid }}^{2k-1}$ in the critical strip

The main subject of this paper is the mean-value of the function $\mathrm{\mid }\zeta (s){\mathrm{\mid }}^{2k-1}$ in the critical strip. On Lindel" of hypothesis we give a solution to this question for some class of disconnected sets. This paper is English version of our paper \cite{5}.