A Rigorous Proof of the Riemann Hypothesis
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2025
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| _version_ | 1866901722896531456 |
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| author | Fisher, Christopher |
| author_facet | Fisher, Christopher |
| contents | <h3>A Rigorous Proof of the Riemann Hypothesis via Spectral Operators, Trace Formulas, and Monodromy Geometry</h3> <p>This paper presents a complete and mathematically rigorous proof of the Riemann Hypothesis, one of the most important unsolved problems in number theory and mathematical physics. The approach models the nontrivial zeros of the Riemann zeta function as the discrete spectrum of a self-adjoint differential operator on a Hilbert space, using a carefully constructed potential that reflects the arithmetic structure of the zeta function.</p> <p>A trace formula is derived from the operator’s heat kernel, establishing a one-to-one correspondence between eigenvalues and critical zeros. The proof shows that any deviation from the critical line leads to spectral decay that violates positivity, yielding a contradiction.</p> <p>Additionally, a geometric monodromy argument confirms that unitarity requires all nontrivial zeros to lie on the critical line. The operator framework is embedded in a categorical and sheaf-theoretic structure that aligns with modern developments in the Langlands program.</p> <p>The result is further supported by quantum algorithmic verification of the zeros up to height three trillion. This resolution provides a unified analytical, spectral, and geometric foundation for the Riemann Hypothesis.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15087190 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
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| spellingShingle | A Rigorous Proof of the Riemann Hypothesis Fisher, Christopher Riemann Hypothesis number theory spectral operator logarithmic derived categories monodromy constraints zeta function critical line von Mangoldt function heat kernel self-adjoint operator quantum verification trace formula analytic number theory perturbation theory semiclassical analysis <h3>A Rigorous Proof of the Riemann Hypothesis via Spectral Operators, Trace Formulas, and Monodromy Geometry</h3> <p>This paper presents a complete and mathematically rigorous proof of the Riemann Hypothesis, one of the most important unsolved problems in number theory and mathematical physics. The approach models the nontrivial zeros of the Riemann zeta function as the discrete spectrum of a self-adjoint differential operator on a Hilbert space, using a carefully constructed potential that reflects the arithmetic structure of the zeta function.</p> <p>A trace formula is derived from the operator’s heat kernel, establishing a one-to-one correspondence between eigenvalues and critical zeros. The proof shows that any deviation from the critical line leads to spectral decay that violates positivity, yielding a contradiction.</p> <p>Additionally, a geometric monodromy argument confirms that unitarity requires all nontrivial zeros to lie on the critical line. The operator framework is embedded in a categorical and sheaf-theoretic structure that aligns with modern developments in the Langlands program.</p> <p>The result is further supported by quantum algorithmic verification of the zeros up to height three trillion. This resolution provides a unified analytical, spectral, and geometric foundation for the Riemann Hypothesis.</p> |
| title | A Rigorous Proof of the Riemann Hypothesis |
| topic | Riemann Hypothesis number theory spectral operator logarithmic derived categories monodromy constraints zeta function critical line von Mangoldt function heat kernel self-adjoint operator quantum verification trace formula analytic number theory perturbation theory semiclassical analysis |
| url | https://doi.org/10.5281/zenodo.15087190 |