Analysis reveals significant zero spacing in Riemann zeta zeros related to topological phase structure, suggesting implications for spectral approaches.
We report magnetometric measurements that reveal field nodes at angular positions 140° and 310° across three materials: neodymium (ferromagnetic), ferrite (ferrimagnetic), and gold (diamagnetic). This consistency across materials with different magnetic properties suggests, but does not yet prove, material-independence. These angles correspond to boundaries defined by the Euler totient function φ(360): phases φ with GCD(φ, 360) > 1 cannot host primes p > 5, by elementary divisibility. Analysis of 195 Riemann zeta zeros (from Odlyzko tables, mapped to phase via t mod 360°) indicates a statistically significant difference in zero spacing between sectors defined by these nodes (t = 2.35, p = 0.02), while prime gaps show no comparable asymmetry. This observation, though preliminary and dependent on the chosen mapping, may be suggestive for spectral approaches to the Riemann Hypothesis.
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Ptak Jan (2025) studied this question.
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