Normalized Spacings between Zeros of Riemann Zeta Function Given by Normalized Maxwell-Boltzmann Distribution

摘要

The implications of a scale invariant model of statistical mechanics to the physical foundations of quantum mechanics and continuum mechanics are described. It is shown that the normalized distribution of spacings between zeros of Riemann zcta function is in close agreement with the normalized Maxwell-Boltzmann distribution function for speed of particles at thermodynamic equilibrium. Possible connections between the distribution of normalized spacings of zeros of Riemann zeta function, the normalized eigenvalues of Gaussian Unitary Ensemble (GUE), and the energy levels in quantum mechanics are discussed.