Systèmes de points, diviseurs et structure fractale

Michel Mendès France; Gérald Tenenbaum

Bulletin de la Société Mathématique de France (1993)

  • Volume: 121, Issue: 2, page 197-225
  • ISSN: 0037-9484

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Mendès France, Michel, and Tenenbaum, Gérald. "Systèmes de points, diviseurs et structure fractale." Bulletin de la Société Mathématique de France 121.2 (1993): 197-225. <http://eudml.org/doc/87665>.

@article{MendèsFrance1993,
author = {Mendès France, Michel, Tenenbaum, Gérald},
journal = {Bulletin de la Société Mathématique de France},
keywords = {fractals; systems of points; distribution of prime divisors; distribution of typical integers; divisors; fractal dimension; Hausdorff dimension; structure of sets of normalized divisors of integers},
language = {fre},
number = {2},
pages = {197-225},
publisher = {Société mathématique de France},
title = {Systèmes de points, diviseurs et structure fractale},
url = {http://eudml.org/doc/87665},
volume = {121},
year = {1993},
}

TY - JOUR
AU - Mendès France, Michel
AU - Tenenbaum, Gérald
TI - Systèmes de points, diviseurs et structure fractale
JO - Bulletin de la Société Mathématique de France
PY - 1993
PB - Société mathématique de France
VL - 121
IS - 2
SP - 197
EP - 225
LA - fre
KW - fractals; systems of points; distribution of prime divisors; distribution of typical integers; divisors; fractal dimension; Hausdorff dimension; structure of sets of normalized divisors of integers
UR - http://eudml.org/doc/87665
ER -

References

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  1. [1] BALOG (A.), ERDÖS (P.) and TENENBAUM (G.). — On arithmetic functions involving consecutive divisors, in Analytic Number Theory, Urbana, 1989, B. Berndt, H. Diamond, H. Halberstam, A. Hildebrand eds., Prog. Math. 85, p. 77-90 Birkhäuser, 1990. Zbl0718.11041
  2. [2] BOVEY (J.D.). — On the size of prime factors of integers, Acta Arith., t. 33, 1977, p. 65-80. Zbl0353.10033MR55 #10406
  3. [3] ERDÖS (P.). — On the distribution function of additive functions, Ann. of Math., t. 47, 1946, p. 1-20. Zbl0061.07902MR7,416c
  4. [4] ERDÖS (P.) et TENENBAUM (G.). — Sur la structure de la suite des diviseurs d'un entier, Ann. Inst. Fourier, t. 31, 1981, p. 17-37. Zbl0437.10020
  5. [5] ERDÖS (P.) et TENENBAUM (G.). — Sur les diviseurs consécutifs d'un entier, Bull. Soc. Math. France, t. 111, 1983, p. 125-145. Zbl0526.10036
  6. [6] ERDÖS (P.) et TENENBAUM (G.). — Sur les fonctions arithmétiques liées aux diviseurs consécutifs, J. Number Theory, t. 31, 1989, p. 285-311. Zbl0676.10030MR90i:11103
  7. [7] HALBERSTAM (H.) and RICHERT (H.-E.). — On a result of R.R. Hall, J. Number Theory (1), t. 11, 1979, p. 76-89. Zbl0395.10048MR80j:10050
  8. [8] HALL (R.R.) and TENENBAUM (G.). — Divisors. — Cambridge University Press, 1988. Zbl0653.10001MR90a:11107
  9. [9] MAIER (H.) and TENENBAUM (G.). — On the set of divisors of an integer, Invent. Math., t. 76, 1984, p. 121-128. Zbl0536.10039MR86b:11057
  10. [10] MANDELBROT (B.B.). — Les objets fractals : forme, hasard et dimension. - Flammarion, Paris 1975 ; 3e édition, 1989. Zbl0900.00018
  11. [11] SHIU (P.). — A Brun-Titchmarsh Theorem for Multiplicative Functions, J. Reine Angew. Math., t. 313, 1980, p. 161-170. Zbl0412.10030MR81h:10065
  12. [12] TENENBAUM (G.). — Lois de répartition des diviseurs 4, Ann. Inst. Fourier, t. 29, 1979, p. 1-15. Zbl0403.10029MR83a:10094c
  13. [13] TENENBAUM (G.). — Un problème de probabilité conditionnelle en arithmétique, Acta Arith., t. 49, 1987, p. 165-187. Zbl0636.10038MR89d:11081
  14. [14] TENENBAUM (G.). — Introduction à la théorie analytique et probabiliste des nombres. - Publications de l'Institut Élie Cartan, Université de Nancy I, 1990. Zbl0788.11001

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