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| Format: | Recurso digital |
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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17564609 |
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Table of Contents:
- <p>A renormalized analytic correspondence between Fredholm determinants and Hermite–Biehler entire functions is established within the **Conservative Motion Theory (CMT)** framework. <br>For $\kappa>0$, a Gaussian reflection–positive operator defines $\Xi_\kappa(E)=\det_2(I-\alpha K_\kappa(E))$ with real, simple zeros. <br>Through torus compactification and Szegő–Widom renormalization, the limit $\kappa\!\to\!0^{+}$ defines $\Xi_0(E)$, preserving real–zero structure under a uniform Hermite–Biehler limit. <br>The coupling $\alpha=1/(2\pi)$ is uniquely determined via Mellin analysis, providing an analytic completion of the Fredholm–de Branges correspondence and a rigorous foundation for real–zero persistence in analytic number theory.</p>