Correlations among the Riemann zeros: Invariance, resurgence, prophecy and self-duality

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dc.creatorLu, W. T.
dc.creatorSridhar, S.
dc.date2004-05-25
dc.date2004-06-02
dc.date.accessioned2026-07-07T05:35:35Z
dc.date.available2026-07-07T05:35:35Z
dc.descriptionWe present a conjecture describing new long range correlations among the Riemann zeros leading to 3 principal features: (i) The spectral auto-correlation is invariant w.r.t. the averaging window. (ii) Resurgence occurs wherein the lowest zeros appear in all auto-correlations. (iii) Suitably defined correlations lead to predictions (prophecy) of new zeros. This conjecture is supported by analytical arguments and confirmed by numerical calculations using 10^{22} zeros computed by Odlyzko. The results lead to a self-duality of the Riemann spectrum similar to the quantum-classical duality observed in billiards.
dc.description16 pages, 10 figures
dc.identifierhttps://arxiv.org/abs/nlin/0405058
dc.identifierhttp://arxiv.org/abs/nlin/0405058
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80745
dc.subjectChaotic Dynamics
dc.subjectMathematical Physics
dc.subjectNumber Theory
dc.titleCorrelations among the Riemann zeros: Invariance, resurgence, prophecy and self-duality
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