An Unexpected Connection Between the Discrete Zeta Function and the Erdos-Straus Conjecture Under Mballa's Conjecture

In this article, we establish an additive decomposition of the discrete zeta function (for $s\in {\mathbb{N}}^{\ast }$, $s>1$), more precisely of the function $4(\zeta (s)-1)$, as a series whose general term is of the form $1\mathrm{/}{x}_n(s)+1\mathrm{/}{y}_n(s)+1\mathrm{/}{z}_n(s)$, where $x_n(s),y_n(s),z_n(s)$ are solutions of the Erdos–Straus conjecture under a personal conjecture (which I will refer to here as Mballa’s Conjecture) that I formulated by parametrization in the article: arXiv:2502.20935. This connection thus builds a bridge between analysis and Egyptian fractions in general, and the Erdos–Straus conjecture in particular.