On the Zeta Resonance Operator and Its Spectrum
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| Format: | Recurso digital |
| Langue: | anglais |
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Zenodo
2025
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| _version_ | 1866901526036873216 |
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| author | Nilsson, Henrik |
| author_facet | Nilsson, Henrik |
| contents | <h3><span><strong>(Version 2 – clarified interpretation)</strong></span></h3> <p>Version 2 of the original Zenodo record <em>“The Zeta Resonance Operator: Toward a Spectral–Analytic Proof of the Riemann Hypothesis.”</em></p> <p>This revision presents the refined mathematical formulation entitled <em>“On the Zeta Resonance Operator and Its Spectrum.”</em> The title, abstract, and language have been updated for clarity and alignment with mathematical-physics standards, while the operator construction and analytical content remain unchanged from Version 1.</p> <p>The framework defines a self-adjoint resonance operator whose eigenvalues correspond to the non-trivial zeros of the Riemann zeta function, satisfying the Hilbert–Pólya conditions of self-adjointness, spectral–arithmetic correspondence, and Weil positivity.</p> <p>The operator is formulated within a four-dimensional representation, as presented in the original work. In subsequent developments, this fourth component is more precisely interpreted as an internal coherence parameter, denoted ζ, rather than as an additional spatial dimension. The four-dimensional formulation is therefore understood as a mathematical embedding of a deeper resonance structure, consistent with later coherence-based formulations in which ζ represents field-depth organization within a three-dimensional spatial manifold.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17497199 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | On the Zeta Resonance Operator and Its Spectrum Nilsson, Henrik Riemann Hypothesis Zeta Resonance Operator Hilbert–Pólya Conjecture Spectral Theory Inverse Spectral Reconstruction Weil Positivity Criterion Gel'fand–Levitan–Marchenko Method Resonance Field Dynamics Physical Interpretation of Zeta Zeros Theoretical Physics Prime Number Spectrum Millennium Prize Problems Unsolved Problems in Mathematics Clay Millennium Problems Quantum Chaos <h3><span><strong>(Version 2 – clarified interpretation)</strong></span></h3> <p>Version 2 of the original Zenodo record <em>“The Zeta Resonance Operator: Toward a Spectral–Analytic Proof of the Riemann Hypothesis.”</em></p> <p>This revision presents the refined mathematical formulation entitled <em>“On the Zeta Resonance Operator and Its Spectrum.”</em> The title, abstract, and language have been updated for clarity and alignment with mathematical-physics standards, while the operator construction and analytical content remain unchanged from Version 1.</p> <p>The framework defines a self-adjoint resonance operator whose eigenvalues correspond to the non-trivial zeros of the Riemann zeta function, satisfying the Hilbert–Pólya conditions of self-adjointness, spectral–arithmetic correspondence, and Weil positivity.</p> <p>The operator is formulated within a four-dimensional representation, as presented in the original work. In subsequent developments, this fourth component is more precisely interpreted as an internal coherence parameter, denoted ζ, rather than as an additional spatial dimension. The four-dimensional formulation is therefore understood as a mathematical embedding of a deeper resonance structure, consistent with later coherence-based formulations in which ζ represents field-depth organization within a three-dimensional spatial manifold.</p> |
| title | On the Zeta Resonance Operator and Its Spectrum |
| topic | Riemann Hypothesis Zeta Resonance Operator Hilbert–Pólya Conjecture Spectral Theory Inverse Spectral Reconstruction Weil Positivity Criterion Gel'fand–Levitan–Marchenko Method Resonance Field Dynamics Physical Interpretation of Zeta Zeros Theoretical Physics Prime Number Spectrum Millennium Prize Problems Unsolved Problems in Mathematics Clay Millennium Problems Quantum Chaos |
| url | https://doi.org/10.5281/zenodo.17497199 |