The references listed below delineate the indispensable conceptual core for the dialogue between quantum chaos, spectral statistics, and Random Matrix Theory, without relying directly on the Riemann Hypothesis as a central axis. They underpin the physical–mathematical framework adopted throughout the book and establish the technical vocabulary and diagnostic criteria employed.
BERRY, M. V. Quantum chaology. Proceedings of the Royal Society of London A, vol. 413, pp. 183–198, 1987.
BERRY, M. V. Regular and irregular semiclassical wavefunctions. Journal of Physics A: Mathematical and General, vol. 10, no. 12, pp. 2083–2091, 1977.
BOHIGAS, O.; GIANNONI, M. J.; SCHMIT, C. Characterization of chaotic quantum spectra and universality of level fluctuation laws. Physical Review Letters, vol. 52, no. 1, pp. 1–4, 1984.
COSTA, A. (2025). The Arithmetic Mirror: Deterministic Emergence of GOE Statistics from the Prime Structure. Zenodo. https://doi.org/10.5281/zenodo.17643156
MEHTA, M. L. Random Matrices. 3rd ed. Amsterdam: Elsevier, 2004.
HAAKE, F. Quantum Signatures of Chaos. 2nd ed. Berlin: Springer, 2001.
BERRY, M. V.; KEATING, J. P. H = xp and the Riemann zeros. Proceedings of the Royal Society of London A, vol. 455, no. 1989, pp. 241–254, 1999.
KEATING, J. P.; SNAITH, N. C. Random matrix theory and ζ(1/2 + it). Communications in Mathematical Physics, vol. 214, pp. 57–89, 2000.
ATAS, Y. Y. et al. Distribution of the ratio of consecutive level spacings in random matrix ensembles. Physical Review Letters, vol. 110, no. 8, 084101, 2013.