%0 Journal Article %T Correlations among the Riemann zeros: Invariance, resurgence, prophecy and self-duality %A W. T. Lu %A S. Sridhar %J Physics %D 2004 %I arXiv %X 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 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. %U http://arxiv.org/abs/nlin/0405058v2