Dirichlet Walks and Center-of-Mass Stability: A Kinematic-Geometric Approach to the Riemann Hypothesis
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| Format: | Recurso digital |
| Language: | English |
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2026
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| _version_ | 1866901215731777536 |
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| author | Shetrit, Aviad |
| author_facet | Shetrit, Aviad |
| contents | <p>This paper develops a kinematic-geometric framework for the Riemann zeta function<br>based on the center-of-mass dynamics of finite Dirichlet sums.</p> <p>Interpreting the partial sums as a weighted Dirichlet walk, we study the accumulation of its normalized center<br>of mass and identify an asymptotic helical structure arising from<br>Euler--Maclaurin summation.</p> <p>Within this framework, zeta zeros are characterized by the disappearance of<br>leading residual wobble in the center-of-mass evolution.</p> <p>Analyzing the induced wobble dynamics, we decompose the forcing into symmetric<br>and asymmetric components and show that the asymmetric contribution vanishes only<br>on the critical line </p> <p>Re(s)=1/2.</p> <p>This yields a geometric rigidity mechanism linking the absence of residual wobble<br>to critical-line localization of nontrivial zeros.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19795908 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Dirichlet Walks and Center-of-Mass Stability: A Kinematic-Geometric Approach to the Riemann Hypothesis Shetrit, Aviad Riemann Hypothesis Dirichlet Series Geometric Number Theory <p>This paper develops a kinematic-geometric framework for the Riemann zeta function<br>based on the center-of-mass dynamics of finite Dirichlet sums.</p> <p>Interpreting the partial sums as a weighted Dirichlet walk, we study the accumulation of its normalized center<br>of mass and identify an asymptotic helical structure arising from<br>Euler--Maclaurin summation.</p> <p>Within this framework, zeta zeros are characterized by the disappearance of<br>leading residual wobble in the center-of-mass evolution.</p> <p>Analyzing the induced wobble dynamics, we decompose the forcing into symmetric<br>and asymmetric components and show that the asymmetric contribution vanishes only<br>on the critical line </p> <p>Re(s)=1/2.</p> <p>This yields a geometric rigidity mechanism linking the absence of residual wobble<br>to critical-line localization of nontrivial zeros.</p> |
| title | Dirichlet Walks and Center-of-Mass Stability: A Kinematic-Geometric Approach to the Riemann Hypothesis |
| topic | Riemann Hypothesis Dirichlet Series Geometric Number Theory |
| url | https://doi.org/10.5281/zenodo.19795908 |