Spectral Realization of the Nontrivial Zeros of the Riemann Zeta Function via a Hermitian Operator Framework
Year: 2025
Type: article
Abstract: We present a spectral construction of a Hermitian operator whose spectrum coincides exactly with the imaginary parts of the nontrivial zeros of the Riemann zeta function The operator, denoted H∞, is defined on a discrete geometric space modeled by a 20-vertex dodecahedral graph, incorporating a discrete Laplacian, an entropy-based coherence potential, and a prime-indexed infinite-order algebraic term derived from Infinity Algebra. We show that H∞ is self-adjoint, spectrally complete, and compatible with the analytic continuation and functional symmetry of ζ(s). A spectral determinant constructed from its eigenvalues matches the Hadamard product representation of ζ 1 + it , and no extraneous roots appear off the critical line. Numerical approximations from a truncated version of the operator validate this correspondence. The construction yields a functional-analytic framework that supports a spectral- theoretic resolution of the Riemann Hypothesis
Institutions: Hellenic Open University, Muni University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4410543290