# Jacob's ladders and infinite set of transmutations of asymptotic complete hybrid formula on level curves in Gauss' plane

## TL;DR

This paper introduces a novel phenomenon where a fixed asymptotic hybrid formula generates infinite transmutations linking the Riemann zeta function's values with moduli of integral and meromorphic functions, revealing new mathematical relationships.

## Contribution

It presents the discovery that each 'mother' hybrid formula produces an infinite set of transmutations connecting zeta function values with other complex functions.

## Key findings

- Infinite transmutations of hybrid formulas are generated from a single mother formula.
- Each transmutation links subsets of |zeta(s)| with moduli of integral and meromorphic functions.
- New relationships in the complex plane are established through these formulas.

## Abstract

In this paper we have obtained new phenomenon lying in the following: every fixed asymptotic complete hybrid formula (we call it as mother formula) generates infinite set of new formulas (transmutations) such that every new formula expresses a close binding between some subset of $\{|\zeta(s)|\}$ and subset of moduli of certain integral and meromorphic functions.