Abstract

We 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 10²² zeros computed by Odlyzko. The results lead to a self-duality of the Riemann spectrum similar to the quantum-classical duality observed in billiards.

Notes

Originally posted at http://arxiv.org/abs/nlin/0405058v2.

Keywords

correlations, Riemann zeros, self-duality, invariance, resurgence, prophecy, nonlinear sciences

Subject Categories

Symmetry (Physics)

Disciplines

Physics

Publication Date

2004

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