# Jacob's ladders and exact meta-functional equations on level curves as global quantitative characteristics of synergetic phenomenons excited by the function $|\zeta({1\over2}+it)|^2$

## TL;DR

This paper introduces a set of fifteen exact meta-functional equations related to the Riemann zeta-function, derived through crossbreeding of hybrid formulas, offering new insights into its level curves and synergetic phenomena.

## Contribution

It presents a novel method of deriving exact meta-functional equations for the Riemann zeta-function using crossbreeding of hybrid formulas, expanding the theoretical framework.

## Key findings

- Fifteen new exact meta-functional equations for the zeta-function
- Identification of level curves as global quantitative characteristics
- Application of crossbreeding to hybrid formulas

## Abstract

In this paper we use operation of crossbreeding on the set of six transmutations of corresponding asymptotic complete hybrid formulas from our previous paper. We obtain in result the set of fifteen exact meta-functional equations. Every of them represents new formula in the theory of the Riemann's zeta-function.