Holographic Realization of Riemann Zeros via a Hilbert-P´olya Operator
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2025
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| _version_ | 1866902240571162624 |
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| author | Li, Y.Y.N. |
| author_facet | Li, Y.Y.N. |
| contents | <p>We propose an exploratory operator model that realizes the imagi-</p> <p>nary parts of the non-trivial Riemann zeta zeros as the eigenvalues of</p> <p>a Schrödinger-type Hermitian operator, inspired by the spectral duality</p> <p>in AdS/CFT holography. The potential of the operator is derived from</p> <p>the AdS/CFT framework, specifically through the boundary projection of</p> <p>bulk quasi-normal modes (QNMs). We compute the eigenvalues using a</p> <p>finite-difference method, achieving a relative error of less than 0.2% for</p> <p>the first 100 Riemann zeros. The spectral trace and associated zeta func-</p> <p>tion are analyzed, showing a numerical correspondence with the Riemann</p> <p>zeta function. This framework, while exploratory, provides a concrete</p> <p>realization of the Hilbert-Pólya conjecture within a holographic context,</p> <p>supported by detailed numerical validations. This work builds on our</p> <p>previous AdS/CFT framework [5].</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15204635 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Holographic Realization of Riemann Zeros via a Hilbert-P´olya Operator Li, Y.Y.N. <p>We propose an exploratory operator model that realizes the imagi-</p> <p>nary parts of the non-trivial Riemann zeta zeros as the eigenvalues of</p> <p>a Schrödinger-type Hermitian operator, inspired by the spectral duality</p> <p>in AdS/CFT holography. The potential of the operator is derived from</p> <p>the AdS/CFT framework, specifically through the boundary projection of</p> <p>bulk quasi-normal modes (QNMs). We compute the eigenvalues using a</p> <p>finite-difference method, achieving a relative error of less than 0.2% for</p> <p>the first 100 Riemann zeros. The spectral trace and associated zeta func-</p> <p>tion are analyzed, showing a numerical correspondence with the Riemann</p> <p>zeta function. This framework, while exploratory, provides a concrete</p> <p>realization of the Hilbert-Pólya conjecture within a holographic context,</p> <p>supported by detailed numerical validations. This work builds on our</p> <p>previous AdS/CFT framework [5].</p> |
| title | Holographic Realization of Riemann Zeros via a Hilbert-P´olya Operator |
| url | https://doi.org/10.5281/zenodo.15204635 |