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

Abstract

The main subject of this paper is the mean-value of the function $|\zeta(s)|^{2k-1}$ 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}.