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

TL;DR

This paper investigates the mean-value of the function |z(s)|^{2k-1} within the critical strip, providing solutions under Lindelf6f hypothesis for certain disconnected sets, advancing understanding of the zeta function's behavior.

Contribution

It offers new results on the mean-value of |z(s)|^{2k-1} under Lindelf6f hypothesis for specific disconnected sets, extending prior work on the zeta function.

Findings

Mean-value results under Lindelf6f hypothesis

Solutions for specific disconnected sets

Enhanced understanding of |z(s)|^{2k-1} behavior

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}.