Sur la probabilité qu'un entier possède un diviseur dans un intervalle donné

G. Tenenbaum

Compositio Mathematica (1984)

  • Volume: 51, Issue: 2, page 243-263
  • ISSN: 0010-437X

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Tenenbaum, G.. "Sur la probabilité qu'un entier possède un diviseur dans un intervalle donné." Compositio Mathematica 51.2 (1984): 243-263. <http://eudml.org/doc/89644>.

@article{Tenenbaum1984,
author = {Tenenbaum, G.},
journal = {Compositio Mathematica},
keywords = {asymptotic formula; distribution of divisors},
language = {fre},
number = {2},
pages = {243-263},
publisher = {Martinus Nijhoff Publishers},
title = {Sur la probabilité qu'un entier possède un diviseur dans un intervalle donné},
url = {http://eudml.org/doc/89644},
volume = {51},
year = {1984},
}

TY - JOUR
AU - Tenenbaum, G.
TI - Sur la probabilité qu'un entier possède un diviseur dans un intervalle donné
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 51
IS - 2
SP - 243
EP - 263
LA - fre
KW - asymptotic formula; distribution of divisors
UR - http://eudml.org/doc/89644
ER -

References

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  2. [2] N.G. de Bruijn: On the number of positive integers ≤ x and free of prime factors &gt; y. Indag. Math.13 (1951) 50-60. Zbl0042.04204
  3. [3] P. Erdös: Note on the sequences of integers none of which are divisible by any other. J. London Math. Soc.10 (1935) 126-128. Zbl0012.05202JFM61.0132.02
  4. [4] P. Erdös: A generalization of a theorem of Besicovitch. J. London Math. Soc.Il (1936) 92-98. Zbl0014.01104JFM62.0154.01
  5. [5] P. Erdös: Sur une inégalité asymptotique en théorie des nombres. Vestnik Leningrad Univ., Serija Mat. Mekh. i Astr. 13 (1960) 41-49 (en russe). 
  6. [6] P. Erdös et R.R. Hall: On the Möbius fonction. J. reine angew. Math.375 (1980) 121-126. Zbl0419.10006
  7. [7] P. Erdös et C. Pomerance: Matching the natural numbers up to n with distinct multiples in another interval. Proc. Nederl. Akad. Wetensch, A83 (2) (1980) 147-161. Zbl0426.10048MR577570
  8. [8] P. Erdös et A. Szemerédi: On multiplicative representations of integers. J. Austral. Math. Soc.21 (Series A) (1976) 418-427. Zbl0327.10004MR417107
  9. [9] P. Erdös et G. Tenenbaum: Sur les diviseurs consécutifs d'un entier, Bull. Soc. Math. de France111, fasc. 2, (1983) à paraître. Zbl0526.10036
  10. [10] G. Halàsz: Remarks to my paper "On the distribution of additive and the mean value of multiplicative arithmetic functions". Acta Math. Acad. Scient. Hung.23 (3-4) (1972) 425-432. Zbl0255.10046MR319931
  11. [11] H. Halberstam et H.-E. Richert: On a result of R.R. Hall. J. Number Theory (1) 11 (1979) 76-89. Zbl0395.10048MR527762
  12. [12] H. Halberstam et K.F. Roth: Sequences, Oxford at the Clarendon Press (1966). Zbl0141.04405MR210679
  13. [13] C. Hooley: On a new technique and its applications to the theory of numbers. Proc. London Math. Soc. (3) 38 (1979) 115-151. Zbl0394.10027MR520975
  14. [14] K.K. Norton: On the number of restricted prime factors of an integer, I. Illinois J. Math.20 (1976) 681-705. Zbl0329.10035MR419382
  15. [15] K.K. Norton: Estimates for partial sums of the exponential series. J. of Math. Analysis and Applications63 (1) 265-296. Zbl0385.41023MR482963
  16. [16] C.L. Stewart: On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers. Proc. of the London Math. Soc. (3) 35 (1977) 425-447. Zbl0389.10014MR491445
  17. [17] G. Tenenbaum: Sur la répartition des diviseurs. Sém. Delange Pisot Poitou 17 (1975/76) no. G14, 5 p.p. Zbl0369.10027
  18. [18] G. Tenenbaum: Lois de répartition des diviseurs, 2. Acta Arithm. (1) 38 (1980) 1-36. Zbl0437.10028MR574122
  19. [19] G. Tenenbaum: Lois de répartition des diviseurs, 3. Acta Arithm. (1) 39 (1981) 19-31. Zbl0472.10043MR638739
  20. [20] G. Tenenbaum: Lois de répartition des diviseurs, 4. Ann. Inst. Fourier (3) 29 (1979) 1-15. Zbl0403.10029MR552957
  21. [21] G. Tenenbaum: Lois de répartition des diviseurs, 5. J. London Math. Soc. (2) 20 (1979) 165-176. Zbl0422.10050MR551441
  22. [22] G. Tenenbaum: Sur la probabilité qu'un entier possède un diviseur dans un intervalle donné. Sém. Théorie des Nombres, Bordeaux (1981/82). Zbl0541.10037

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