Jacob's ladders and properties of complete additivity and complete multiplicativity in the set of reverse iterated integrals (energies)

TL;DR

This paper introduces new integral identities related to the Riemann zeta function, demonstrating properties of complete additivity and multiplicativity within reverse iterated integrals, advancing understanding of these mathematical structures.

Contribution

It presents novel integral identities and establishes properties of complete additivity and multiplicativity in reverse iterated integrals associated with the Riemann zeta function.

Findings

New integral identities for the Riemann zeta function on the critical line

Establishment of $\sigma$-additivity and $\sigma$-multiplicativity in reverse iterated integrals

Enhanced understanding of the behavior of energies related to the zeta function

Abstract

New class of integral identities concerning constraints on behavior of the Riemann's zeta function on the critical line is introduced in this paper. Namely, we have obtained new kind of $\sigma$-additivity and $\sigma$-multiplicativity in the class of reverse iterated integrals (energies).