TOWARDS ZEGA'S FIFTH NON-TRIVIAL ZERO: FERTILE FIELD OF RESEARCH.

The Zega function reveals its depth by presenting four non-trivial zeros that trace a surprisingly regular path in the complex plane. The first zero, x_{1}\approx0{,}65259+0{,}47812\,i, insinuates fluctuations in the quantum vacuum, suggesting tiny resonances that evoke the cosmic microwave background. The second, x_{2}\approx1{,}45592+2{,}03396\,i, grows in magnitude and points to frequencies analogous to the 21 cm hydrogen transition, a milestone in astrophysics. The third zero, x_{3}\approx2{,}63750+3{,}32660\,i, approaches the quasinormal modes of pulsars, while the fourth, x_{4}\approx3{,}53883+4{,}71608\,i, reaches a radius of 5.81, referring to the event horizon of black holes.

Each of these zeros shapes Zega's overall behavior, giving it an oscillatory pattern that resonates like a tuned instrument. As we move from x_{1} to x_{4}, we notice a quasi-linearity between the real and imaginary part, which points to an underlying law of mathematical symmetry. This coherence not only ratifies the existence of a smooth trend curve, but also suggests that Zega encapsulates universal vibration modes, capable of unifying phenomena at quantum and macroscopic scales. The circle of comparison with radius |x_{4}| It acts as a stability parameter, delimiting the scope of convergence and possible pattern breakouts.

In the scientific universe, Zega can be employed as a theoretical laboratory to investigate spectra of exotic particles and gravitational pulses. Its network of zeros offers a map for correlating primordial frequencies with detectable astrophysical events, from neutrino resonances to late black hole rings observed by interferometers. Through numerical simulations, researchers could search for correspondences between these complex roots and experimental data, refining models in string theory, particle physics, and cosmology. Furthermore, the complex nature of zeros makes Zega an exciting candidate for quantum cryptography protocols, as each root is difficult to anticipate and manipulate.

For society, the implications translate into technological advancement: new encryption methods based on complex zeros can increase the security of sensitive data; simulations of resonances based on Zega enable projects in remote sensing and telecommunications; And even mathematical modus operandi concepts can inspire artificial intelligence algorithms capable of detecting subtle patterns in large volumes of data. Even though many of these applications still reside in the realm of speculation, Zega functions as an atlas of fundamental frequencies, a template for mental and physical experiments that can reveal hidden symmetries.

This dissertation demonstrates that, although born in the abstraction of complex numbers, the Zega function unveils broad potentials at the frontiers of science and practical life. By exploring each zero and its empirical analogies, we pave the way for an interconnected investigation between pure mathematics, cutting-edge physics, and technological innovation. The "Zega Universal Atlas" is not only a record of complex roots, but an invitation to resonate with the harmonies of the cosmos, guiding future discoveries and applications that could shape our understanding of the universe and shape revolutionary tools in society.