# Jacob's ladders and the set of elementary meta-functional equations giving new kind of interactions of $\zeta(s)$ with itself

## TL;DR

This paper introduces a novel set of elementary meta-functional equations that describe new interactions of the Riemann zeta-function with itself, derived from elementary functions on critical strips.

## Contribution

It develops a new method of grafting elementary functions to generate meta-functional equations involving the zeta-function, revealing new interaction structures.

## Key findings

- Set of elementary meta-functional equations derived
- New interactions of $ta(s)$ with itself identified
- Method of grafting elementary functions established

## Abstract

In this paper we obtain the set of grafts from some set of 12 elementary functions on 12 critical strips. We make use this directly for grafting of elements of the corresponding set of $\zeta$-factorization formulas. This procedure gives the set of elementary meta-functional equations that represents the set of elementary interactions of the Riemann's zeta-function with itself.