Jacob's ladders and invariant set of constraints for the reversely iterated integrals (energies) in the theory of the Riemann zeta-function

TL;DR

This paper introduces a new continuum of local and non-local equalities for reversely iterated integrals related to the Riemann zeta-function, providing constraints on its behavior as t approaches infinity.

Contribution

It extends the set of known equalities by adding local constraints, forming an invariant set for the energies in the theory of the Riemann zeta-function.

Findings

Established a continuum of equalities for reversely iterated integrals

Created an invariant set of constraints on the zeta-function's behavior

Enhanced understanding of the energy distribution related to the zeta-function

Abstract

In this paper we obtain an extension of the set of non-local equalities by adding to it new set of local equalities. Namely, we obtain an invariant set of equalities on the set of reversely iterated integrals (energies). In other words, we obtain a new continuum set of constraints on behaviour of the function $\zf,\ t\to\infty$.