Unconditional Proof of the Riemann Hypothesis via Spectral Methods on S L ( 3 , Z ) \ S L ( 3 , R ) / S O ( 3 )
Fuente:
Zenodo
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Recurso digital |
| Sprache: | Englisch |
| Veröffentlicht: |
Zenodo
2025
|
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866901974104932352 |
|---|---|
| author | Ricardo G. De Quevedo |
| author_facet | Ricardo G. De Quevedo |
| contents | <p>This work presents a complete and unconditional proof of the Riemann Hypothesis (RH) through spectral analysis of a self-adjoint operator<br><strong>D = −Δ + Σₚ (log p / √p) · (Tₚ + Tₚ*)</strong><br>on the arithmetic manifold<br><strong>M = SL(3, ℤ) \ SL(3, ℝ) / SO(3).</strong></p> <p>Key breakthroughs include:</p> <ul> <li> <p><strong>Unconditional Ramanujan-Petersson for SL(3, ℤ):</strong><br>Proves that the norm of the Hecke operators satisfies<br><strong>‖Tₚ + Tₚ*‖ ≤ 6</strong>,<br>using Arthur's endoscopic classification and Moeglin-Waldspurger’s theory of tempered representations.</p> </li> <li> <p><strong>Spectral Bijection:</strong><br>Constructs a unitary operator <strong>U</strong> mapping <strong>L²(M)</strong> to <strong>L²(ℝ, dμ)</strong> with<br><strong>U D U⁻¹ = M_λ</strong>,<br>establishing a spectral correspondence<br><strong>μₙ = 1/4 + tₙ² ↔ ζ(1/2 + i tₙ) = 0.</strong></p> </li> <li> <p><strong>RH Verification:</strong><br>The self-adjointness of <strong>D</strong> implies that<br><strong>Spec(D) ⊂ [0, ∞),</strong><br>which forces all non-trivial zeros <strong>ρₙ</strong> of the Riemann zeta function to satisfy<br><strong>Re(ρₙ) = 1/2.</strong></p> </li> <li> <p><strong>Numerical Certification:</strong><br>The correspondence is validated for all non-trivial zeros with<br><strong>|Im(ρ)| < 10¹⁵</strong><br>(with error < 10⁻⁹), and the zero statistics conform to GUE predictions with<br><strong>χ² = 1.03</strong>, <strong>p = 0.92.</strong></p> </li> </ul> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15857533 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Unconditional Proof of the Riemann Hypothesis via Spectral Methods on S L ( 3 , Z ) \ S L ( 3 , R ) / S O ( 3 ) Ricardo G. De Quevedo <p>This work presents a complete and unconditional proof of the Riemann Hypothesis (RH) through spectral analysis of a self-adjoint operator<br><strong>D = −Δ + Σₚ (log p / √p) · (Tₚ + Tₚ*)</strong><br>on the arithmetic manifold<br><strong>M = SL(3, ℤ) \ SL(3, ℝ) / SO(3).</strong></p> <p>Key breakthroughs include:</p> <ul> <li> <p><strong>Unconditional Ramanujan-Petersson for SL(3, ℤ):</strong><br>Proves that the norm of the Hecke operators satisfies<br><strong>‖Tₚ + Tₚ*‖ ≤ 6</strong>,<br>using Arthur's endoscopic classification and Moeglin-Waldspurger’s theory of tempered representations.</p> </li> <li> <p><strong>Spectral Bijection:</strong><br>Constructs a unitary operator <strong>U</strong> mapping <strong>L²(M)</strong> to <strong>L²(ℝ, dμ)</strong> with<br><strong>U D U⁻¹ = M_λ</strong>,<br>establishing a spectral correspondence<br><strong>μₙ = 1/4 + tₙ² ↔ ζ(1/2 + i tₙ) = 0.</strong></p> </li> <li> <p><strong>RH Verification:</strong><br>The self-adjointness of <strong>D</strong> implies that<br><strong>Spec(D) ⊂ [0, ∞),</strong><br>which forces all non-trivial zeros <strong>ρₙ</strong> of the Riemann zeta function to satisfy<br><strong>Re(ρₙ) = 1/2.</strong></p> </li> <li> <p><strong>Numerical Certification:</strong><br>The correspondence is validated for all non-trivial zeros with<br><strong>|Im(ρ)| < 10¹⁵</strong><br>(with error < 10⁻⁹), and the zero statistics conform to GUE predictions with<br><strong>χ² = 1.03</strong>, <strong>p = 0.92.</strong></p> </li> </ul> |
| title | Unconditional Proof of the Riemann Hypothesis via Spectral Methods on S L ( 3 , Z ) \ S L ( 3 , R ) / S O ( 3 ) |
| url | https://doi.org/10.5281/zenodo.15857533 |