Properties of the sequence $\{Z[t_{\nu }(\tau )]\}$, Jacob's ladders and new kind of infinite set of metamorphosis of main multiform

Abstract

In this paper we study properties of some sums of members of the sequence $\{Z[t_{\nu }(\tau )]\}$. Our results are expressed in statements proving essential influence of the Lindel\" of hypothesis on corresponding formulae. In this paper: the parts 1 -- 6 are English version of our paper \cite{6}, and the part 7 of this work contains current results, namely new set of metamorphosis of the main multiform from our paper \cite{7}.