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

TL;DR

This paper investigates properties of a specific sequence related to Jacob's ladders, explores the influence of the Lindelöf hypothesis on related formulas, and introduces a new set of transformations of a main multiform.

Contribution

It presents new results on the sequence's sums, demonstrates the impact of the Lindelöf hypothesis, and introduces a novel set of metamorphoses of the main multiform.

Findings

Influence of Lindelöf hypothesis on sequence properties

New set of metamorphoses of the main multiform

Results extend previous work with current findings

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}.