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Number Theory and Physics pp 276–293Cite as

Statistical Theory of Numbers

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Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 47))

Abstract

This article is three-sided: it is a pedestrian introduction to the Riemann hypothesis in the case of the classical zeta function, it provides also an elementary presentation of Quantum Statistical Mechanics and finally it is an attempt to present the reader with a precise dictionary between the fields of number theory -additive or multiplicative- on the one hand and of thermodynamics of “solved quantum systems” on the other, the physical terms mentioned in the mathematical part will be defined in the Physics section.

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References

  1. B. Riemann, Monatsberichte der Berliner Akad. (1859) November.

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  2. R. Hagedorn, Suppl. Nuovo Cimento 3 (1965) 147. See also Yu. B. Rumer, J. Exp. Theor. Phys. 38 (1960) 1899.

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  10. B.L. Julia, in preparation,

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  11. B.L. Julia, 1985 unpublished. B.L. Julia, Journal de Physique 50 (1989) 1371. D. Spector, Utrecht preprint THU ‘88/41. J. Hannay, unpublished according to M. Berry. G.W. Mackey, Unitary group representation in Physics, Probability and number theory Benjamin, Reading 1978. Unknown…

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Author information

Authors and Affiliations

  1. Laboratoire de Physique Théorique de l’Ecole Supérieure, 24, Rue Lhomond, F-75231, Paris Cedex 05, France

    B. Julia

Authors
  1. B. Julia
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Editor information

Editors and Affiliations

  1. Service de Physique Théorique, C.E.N Saclay, F-91191, Gif-sur-Yvette Cedex, France

    Jean-Marc Luck  & Pierre Moussa  & 

  2. Institut Henri-Poincaré, Problèmes Diophantiens, Université de Paris 6, F-75231, Paris Cedex 05, France

    Michel Waldschmidt

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© 1990 Springer-Verlag Berlin Heidelberg

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Julia, B. (1990). Statistical Theory of Numbers. In: Luck, JM., Moussa, P., Waldschmidt, M. (eds) Number Theory and Physics. Springer Proceedings in Physics, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75405-0_30

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  • DOI: https://doi.org/10.1007/978-3-642-75405-0_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-75407-4

  • Online ISBN: 978-3-642-75405-0

  • eBook Packages: Springer Book Archive

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