Bewaard in:
| Hoofdauteur: | |
|---|---|
| Formaat: | Recurso digital |
| Taal: | Engels |
| Gepubliceerd in: |
Zenodo
2026
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| Onderwerpen: | |
| Online toegang: | https://doi.org/10.5281/zenodo.19965225 |
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Inhoudsopgave:
- <p>Starting from a single operation — the polar decomposition of the canonical logarithm applied to the Euler product — we derive the topological structure of the critical line of the Riemann zeta function in the <em>b</em>-plane of the specialization map Φ: <em>b</em> ↦ <em>p</em><sup>−<em>s</em></sup> introduced in Paper 1. The unconditional content — tori at every depth, phase coordinates, incommensurability, density, and the strict complexity of zeros — follows from one theorem whose only inputs are the canonical logarithm, the Fundamental Theorem of Arithmetic, and the Kronecker–Weyl equidistribution theorem. The conditional content — the critical circles, the Bohr torus at σ = 1/2, the supercritical/subcritical partition at |<em>b</em>| = 1/2, the spectral compression, and the phase-suppression mechanism — requires one additional datum: the involution ρ(<em>s</em>) = 1 − <em>s</em> from Riemann's functional equation, which depends on the archimedean factor Λ<sub>∞</sub>(<em>s</em>) = π<sup>−<em>s</em>/2</sup> Γ(<em>s</em>/2). This factor is identified as the unique obstruction to closing the chain from the elementary traversals of Paper 1 to the functional equation. Five independent appearances of 1/2 are documented and classified by epistemic status.</p>