Jacob's ladders and multiplicative algebra of reversely iterated integrals (energies) on the critical line

TL;DR

This paper proves a logarithmic formula for reversely iterated integrals (energies) on the critical line, showing that integral powers of ln T appear on both input and output, revealing a multiplicative algebraic structure.

Contribution

It introduces a new logarithmic formula for reversely iterated integrals on the critical line, demonstrating their algebraic properties involving powers of ln T.

Findings

Integral powers of ln T are contained in the reversely iterated integrals

A multiplicative algebra structure of these integrals is established

The results apply to energies on the critical line

Abstract

Certain completely logarithmic formula for a set of reversely iterated integrals (energies) is proved in this paper. Namely, in this case we have that integral powers of $\ln T$ are contained on input as well as on output of corresponding integrals (energies).