Spectral realization of the nontrivial zeros of the Riemann Zeta function via a Hermitian operator framework
| dc.contributor.author | Valamontes, Antonios | |
| dc.contributor.author | Adamopoulos, Ioannis | |
| dc.contributor.author | Ali, Guma | |
| dc.date.accessioned | 2025-12-17T13:48:28Z | |
| dc.date.available | 2025-12-17T13:48:28Z | |
| dc.date.issued | 2025-05-18 | |
| dc.description | This research develops a spectral construction of a Hermitian operator whose spectrum exactly matches the imaginary parts of the nontrivial zeros of the Riemann zeta function, bridging concepts in operator theory and analytic number theory with potential applications in mathematical physics. The work advances understanding of deep mathematical structures and may inspire new techniques in complex analysis and spectral theory. The study supports SDG 4 on quality education by advancing higher-level mathematical knowledge and critical thinking, and SDG 9 on industry, innovation, and infrastructure by fostering advanced analytical tools. | |
| dc.description.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 | |
| dc.identifier.citation | Valamontes, A., Adamopoulos, I., & Ali, G. (2025). Spectral realization of the nontrivial zeros of the Riemann Zeta function via a Hermitian operator framework. Babylonian Journal of Mathematics, 2025, 50-60. | |
| dc.identifier.issn | 3006-113X | |
| dc.identifier.uri | https://dir.muni.ac.ug/handle/20.500.12260/829 | |
| dc.language.iso | en | |
| dc.publisher | Mesopotamian Academic Press | |
| dc.subject | Riemann Hypothesis | |
| dc.subject | Hermitian Operator | |
| dc.subject | Spectral Theory | |
| dc.subject | Zeta Function | |
| dc.subject | Infinity Algebra | |
| dc.title | Spectral realization of the nontrivial zeros of the Riemann Zeta function via a Hermitian operator framework | |
| dc.type | Article |