Théories statistique et thermodynamique des nombres

B. L. Julia

Recherche Coopérative sur Programme n°25 (1993)

  • Volume: 44, page 113-125

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Julia, B. L.. "Théories statistique et thermodynamique des nombres." Recherche Coopérative sur Programme n°25 44 (1993): 113-125. <http://eudml.org/doc/274900>.

@article{Julia1993,
author = {Julia, B. L.},
journal = {Recherche Coopérative sur Programme n°25},
language = {eng},
pages = {113-125},
publisher = {Institut de Recherche Mathématique Avancée - Université Louis Pasteur},
title = {Théories statistique et thermodynamique des nombres},
url = {http://eudml.org/doc/274900},
volume = {44},
year = {1993},
}

TY - JOUR
AU - Julia, B. L.
TI - Théories statistique et thermodynamique des nombres
JO - Recherche Coopérative sur Programme n°25
PY - 1993
PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
VL - 44
SP - 113
EP - 125
LA - eng
UR - http://eudml.org/doc/274900
ER -

References

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  1. [1] B. Julia, SpringerProceedings in Physics47, "Number theory and Physics" ed. J.-M. Luck et al. p. 276 (1990) Zbl0727.11033MR1058443
  2. see also B. JuliaJ. de Phys.50 (1989) 1371. MR1011424
  3. [2] G.H. Hardy, Ramanujan Cambridge U.P. (1940). The rigorous estimate for this asymptotic behavior can be found in : 
  4. [3] E. Wright, Acta Math.63 (1934) 143. Zbl0009.30001MR1555393JFM60.0135.01
  5. [4] B. Julia, to appear in Physica A, Thermodynamic limit in number theory : Riemann-Beurling gases. Zbl0810.11077MR1265190
  6. [5] W.J. Ellison, Les nombres premiers, Hermann (1975). Zbl0313.10001MR417077
  7. [6] G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Published by Université Nancy 1 (1990). Zbl0880.11001
  8. [7] H. Bateman, A. Erdélyi et al., Tables of Integral Transforms, vol.1 (1954) McGraw-Hill. Zbl0058.34103
  9. [8] M. Abramowitz and I. Stegun, Handbook of mathematical functions, Dover (1972). 
  10. [9] H. Bateman, A. Erdélyi, Higher transcendental functions I, McGraw-Hill (1953). Zbl0052.29502
  11. [10] M. E. Fisher, in Lectures in Theoretical PhysicsVIIc, Boulder (1965), University of Colorado Press. 
  12. [11] H. P. McKean, J. Math. Phys.5 (1964) 775. 
  13. [12] D. Ruelle, Comm. Math. Phys.31 (1973) 265. Zbl1125.82311MR353912
  14. [13] L. G. Sathe, J. Indian Math. Soc.17 (1953) 63 Zbl0050.27102MR56625
  15. A. Selberg, ibidem 18 (1954) 83 Zbl0057.28502MR67143
  16. H. Delange, Bull. Sc. math.83 (1959) 101. Zbl0106.03305MR113836
  17. [14] B. Julia in preparation. 

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