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The Zeta Resonance Operator Toward a Spectral–Analytic Proof of the Riemann Hypothesis

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Autore principale:	Nilsson, Henrik
Natura:	Recurso digital
Lingua:	inglese
Pubblicazione:	Zenodo 2025
Soggetti:	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
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_version_	1866901525335375872
author	Nilsson, Henrik
author_facet	Nilsson, Henrik
contents	<p>This preprint introduces the <em>Zeta Resonance Operator</em>, a self-adjoint Schrödinger-type resonance operator whose spectrum reproduces the imaginary parts of the non-trivial zeros of the Riemann zeta function.<br>By combining the Hilbert–Pólya conjecture with a four-dimensional resonance framework, the study bridges number theory and physics through spectral analysis.<br>The operator’s potential is reconstructed via the Gel’fand–Levitan–Marchenko inverse spectral method, its trace reproduces the explicit formula for ζ(s), and its intrinsic positivity corresponds to Weil’s criterion—together fulfilling all three classical pillars required for the Riemann Hypothesis.<br>Numerical reconstructions confirm the theoretical spectrum to within parts-per-thousand precision, providing analytic and empirical support for the model.</p>
format	Recurso digital
id	zenodo_https___doi_org_10_5281_zenodo_17362962
institution	Zenodo
language	eng
publishDate	2025
publisher	Zenodo
record_format	zenodo
spellingShingle	The Zeta Resonance Operator Toward a Spectral–Analytic Proof of the Riemann Hypothesis 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 <p>This preprint introduces the <em>Zeta Resonance Operator</em>, a self-adjoint Schrödinger-type resonance operator whose spectrum reproduces the imaginary parts of the non-trivial zeros of the Riemann zeta function.<br>By combining the Hilbert–Pólya conjecture with a four-dimensional resonance framework, the study bridges number theory and physics through spectral analysis.<br>The operator’s potential is reconstructed via the Gel’fand–Levitan–Marchenko inverse spectral method, its trace reproduces the explicit formula for ζ(s), and its intrinsic positivity corresponds to Weil’s criterion—together fulfilling all three classical pillars required for the Riemann Hypothesis.<br>Numerical reconstructions confirm the theoretical spectrum to within parts-per-thousand precision, providing analytic and empirical support for the model.</p>
title	The Zeta Resonance Operator Toward a Spectral–Analytic Proof of the Riemann Hypothesis
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.17362962