Quelques exemples de suites unimodales en théorie des nombres

Michel Balazard

Journal de théorie des nombres de Bordeaux (1990)

  • Volume: 2, Issue: 1, page 13-30
  • ISSN: 1246-7405

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Balazard, Michel. "Quelques exemples de suites unimodales en théorie des nombres." Journal de théorie des nombres de Bordeaux 2.1 (1990): 13-30. <http://eudml.org/doc/93507>.

@article{Balazard1990,
author = {Balazard, Michel},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {unimodal sequences; partition functions; arithmetic counting functions; unimodality},
language = {fre},
number = {1},
pages = {13-30},
publisher = {Université Bordeaux I},
title = {Quelques exemples de suites unimodales en théorie des nombres},
url = {http://eudml.org/doc/93507},
volume = {2},
year = {1990},
}

TY - JOUR
AU - Balazard, Michel
TI - Quelques exemples de suites unimodales en théorie des nombres
JO - Journal de théorie des nombres de Bordeaux
PY - 1990
PB - Université Bordeaux I
VL - 2
IS - 1
SP - 13
EP - 30
LA - fre
KW - unimodal sequences; partition functions; arithmetic counting functions; unimodality
UR - http://eudml.org/doc/93507
ER -

References

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  2. 2 G.E. Andrews, The theory of partitions, Addison-Wesley (1976), Reading. Zbl0371.10001MR557013
  3. 3 M. Balazard, H. Delange et J.-L. Nicolas, Sur le nombre de facteurs premiers des entiers, C.R.A.S.306 série I (1988), 511-514. Zbl0644.10032MR941613
  4. 4 M. Balazard, Comportement statistique du nombre de facteurs premiers des entiers, Séminaire de Th. des Nombres, Paris 1987-1988, (1990), 1-21, Birkhaüser. Zbl0689.10047MR1042762
  5. 5 M. Balazard, Unimodalité de la distribution du nombre des diviseurs premiers d'un entier. A paraître aux Annales de l'Institut Fourier. Zbl0711.11030
  6. 6 L. Comtet, Analyse combinatoire (1970), P.U.F, Paris. Zbl0221.05001
  7. 7 S. Dharmadikari et K. Joag-Dev, Unimodality, convexity and applications (1988), Academic Press, New-York. Zbl0646.62008MR954608
  8. 8 P. Erdös, On the integers having exactly k prime factors, Annals of Math.49 (1948), 53-66. Zbl0030.29604MR23279
  9. 9 P. Erdös et G. Tenenbaum, Sur les densités de certaines suites d'entiers, Proc. London Math. Soc. (3)59 (1989), 417-438. Zbl0694.10040MR1014865
  10. 10 H. Gerber et J. Keilson, Some results for discrete unimodality, J. Amer. Statist. Assoc.66 (1971), 386-389. Zbl0236.60017
  11. 11 D. Hensley, The distribution of round numbers, Proc. London Math. Soc. (3) 54 (1987), 412-444. Zbl0588.10047MR879393
  12. 12 A. Hildebrand et G. Tenenbaum, On the number of prime factors of an integer, Duke Math. J.56 (1988), 471-501. Zbl0655.10036MR948530
  13. 13 J.W. Hughes, Lie algebraic proofs of some theorems on partitions, Number Theory and Algebra (H. Zassenhaus, ed.) (1977), Academic Press, New-York. Zbl0372.10010MR491213
  14. 14 J.-L. Nicolas, Sur la distribution des entiers ayant une quantité fixée de facteurs premiers, Acta Arith.44 (1984), 191-200. Zbl0512.10034MR774099
  15. 15 A.M. Odlyzko et L.B. Richmond, On the compositions of an integer, Combinatorial Mathematics VII. Proceedings (1979), 199-210, (R.W. Robinson et al. ed.). Springer Lecture Notes 829. Zbl0451.05009MR611195
  16. 16 A.M. Odlyzko et L.B. Richmond, On the unimodality of some partition polynomials, Europ. J. Combinatorics2 (1982), 69-84. Zbl0482.10015MR656013
  17. 17 A.M. Odlyzko et L.B. Richmond, On the unimodality of high powers of discrete distributions, Annals of Probability13 (1985), 299-306. Zbl0561.60021MR770644
  18. 18 C. Pomerance, On the distribution of round numbers, Number Theory (K. Alladi ed.), (Proc. Ootacamund, India, 1984), 173-200, Springer Lecture Notes 1122. Zbl0565.10038MR797790
  19. 19 K.F. Roth et G. Szekeres, Some asymptotic formulae in the theory of partitions, Quart. J. Math. Oxford (2) 5 (1954), 241-259. Zbl0057.03902MR67913
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  23. 23 G. Szekeres, Some asymptotic formulae in the theory of partitions (II), Quart. J. Math. Oxford (2) 4 (1953), 96-111. Zbl0050.04101MR57279

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