Self-Referential Encoding in Zeta Function Theory - Analysis of the Case When Parameter $s$ Encodes the Zeta Algorithm
Year: 2025
Type: article
Abstract: This paper systematically investigates the mathematical structure of the complex parameter $s$ in the Riemann zeta function as a self-referential encoding, particularly the deep recursive phenomena that arise when $s$ itself encodes the algorithm for computing $\zeta(s)$. Through an extended form of Voronin's universality theorem, we prove the existence of special complex numbers $s^*$ such that $\zeta(s^*)$ encodes the algorithm for computing the zeta function itself, thereby forming a complete self-referential loop. This self-referential structure not only produces Banach fixed points and strange loop structures mathematically, but also corresponds to black hole horizons, holographic encoding, and quantum entanglement self-similarity at the physical level. We establish a complete theoretical framework from pure mathematical functional equation enhancement to operator self-adjointness in Hilbert space, and prove the profound connections between this self-referential encoding and Gödel's incompleteness theorems, the halting problem, and the Riemann hypothesis. This research reveals the essential unity of computation, geometry, and quantum mechanics at the level of self-referential encoding, providing a new mathematical foundation for understanding the computational ontology of the universe.
Authors: Ma, Haobo, Zhang, Wenlin
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7090163381
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