### Abstract

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 zeta 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.

Original language | English |
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Title of host publication | Proceedings of the American Conference on Applied Mathematics (AMERICAN-MATH '10) |

Editors | Stephen Lagakos, Leonid Perlovsky, Manoj Jha, Brindusa Covaci, Azami Zaharim, Nikos Mastorakis |

Publisher | WSEAS Press |

ISBN (Print) | 9789604741502 |

State | Published - 2010 |

Event | The American Conference on Applied Mathematics (AMERICAN-MATH '10) - Cambridge, Massachusetts Duration: Jan 1 2010 → … |

### Conference

Conference | The American Conference on Applied Mathematics (AMERICAN-MATH '10) |
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Period | 1/1/10 → … |

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## Cite this

Sohrab, S. H. (2010). Normalized spacings between zeros of Riemann zeta function given by normalized Maxwell-Boltzmann distribution. In S. Lagakos, L. Perlovsky, M. Jha, B. Covaci, A. Zaharim, & N. Mastorakis (Eds.),

*Proceedings of the American Conference on Applied Mathematics (AMERICAN-MATH '10)*WSEAS Press.