Jacob's ladders and new families of $\zeta$-kindred real continuous functions

TL;DR

This paper introduces a novel method using crossbreeding of $$-factorization formulas to identify new families of real continuous functions related to the Riemann zeta function.

Contribution

It presents a new approach to generate and select $$-kindred functions via hybrid formulas derived from $$-factorization, expanding the understanding of zeta-related functions.

Findings

Development of complete hybrid formulas as criteria for function selection

Identification of new families of $$-kindred functions

Advancement in the analytical methods related to the Riemann zeta function

Abstract

In this paper we obtain, by our method of crossbreeding in certain set of $\zeta$-factorization formulas, the corresponding complete hybrid formulas. These are playing the role of criterion for selection of new families of $\zeta$-kindred real continuous functions.