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.
Keywords
correlations, Riemann zeros, self-duality, invariance, resurgence, prophecy, nonlinear sciences
Subject Categories
Symmetry (Physics)
Disciplines
Physics
Publication Date
2004
Permanent URL
Recommended Citation
Lu, W. T. and Sridhar, S., "Correlations among the Riemann zeros: Invariance, resurgence, prophecy and self-duality" (2004). Physics Faculty Publications. Paper 79. http://hdl.handle.net/2047/d20000432
Click button above to open, or right-click to save.
Notes
Originally posted at http://arxiv.org/abs/nlin/0405058v2.