Jacob's ladders, crossbreeding, secondary crossbreeding and synergetic phenomena generated by Riemann's zeta-function and some elementary functions on disconnected sets of the critical line

TL;DR

This paper introduces a new hybrid formula demonstrating the synergistic interaction between elementary functions and the Riemann zeta-function on disconnected sets of the critical line, with comparisons to chemical reactions.

Contribution

It presents a novel complete hybrid formula for zeta-factorization, revealing synergetic phenomena on the critical line, and compares this mathematical behavior to chemical reactions.

Findings

New hybrid formula for zeta-factorization

Demonstration of synergetic cooperation between functions

Comparison with chemical reaction phenomena

Abstract

In this paper we obtain new complete hybrid formula for corresponding class of $\zeta$-factorization formulas. We demonstrate that this formula is the synergetic one. Namely, this one describes the cooperation between some class of elementary functions and Riemann's zeta-function on a class of disconnected sets on the critical line. Some comparizon between this pure mathematical phenomenon and the Belousov-Zhabotinski chemical reaction is added. \centering DEDICATED TO 110th ANNIVERSARY OF HARDY'S PURE MATHEMATICS