A Prime–Resonance Hilbert–Polya Operator and the Riemann Hypothesis
Year: 2025
Type: article
Abstract: We construct a self-adjoint operator on a prime-based Hilbert space whose spectral determinant matches the completed Riemann ξ-function on the critical line. This operator arises naturally within a prime-resonance framework where primes serve as fundamental eigenstates and entropy-driven stabilization enforces spectral alignment. Using a block chiral form, calibrated prime-power trace identity, and functional antiuni- tary symmetry, we prove that all non-trivial zeros of ζ(s) lie on Rs = 12. This provides a resolution of the Riemann Hypothesis via the Hilbert–Po ́lya strategy, extended with resonance and entropy considerations.
Author: Schepis, Sebastian
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7083629174
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