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| Autor principal: | |
|---|---|
| Format: | Recurso digital |
| Idioma: | anglès |
| Publicat: |
Zenodo
2025
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| Accés en línia: | https://doi.org/10.5281/zenodo.15857533 |
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- <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>