On the frequencies of large values of divisor functions

Karl K. Norton

Acta Arithmetica (1994)

  • Volume: 68, Issue: 3, page 219-244
  • ISSN: 0065-1036

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Karl K. Norton. "On the frequencies of large values of divisor functions." Acta Arithmetica 68.3 (1994): 219-244. <http://eudml.org/doc/206657>.

@article{KarlK1994,
author = {Karl K. Norton},
journal = {Acta Arithmetica},
keywords = {distribution of large values; multiplicative function; number of ordered -tuples; upper bounds; lower bounds},
language = {eng},
number = {3},
pages = {219-244},
title = {On the frequencies of large values of divisor functions},
url = {http://eudml.org/doc/206657},
volume = {68},
year = {1994},
}

TY - JOUR
AU - Karl K. Norton
TI - On the frequencies of large values of divisor functions
JO - Acta Arithmetica
PY - 1994
VL - 68
IS - 3
SP - 219
EP - 244
LA - eng
KW - distribution of large values; multiplicative function; number of ordered -tuples; upper bounds; lower bounds
UR - http://eudml.org/doc/206657
ER -

References

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  1. [1] M. Balazard, Comportement statistique du nombre de facteurs premiers des entiers, in: Séminaire de Théorie des Nombres, Paris 1987-88, Progr. Math. 81, Birkhäuser, Boston, 1990, 1-21. 
  2. [2] M. Balazard, Remarques sur un théorème de G. Halász et A. Sárközy, Bull. Soc. Math. France 117 (1989), 389-413. 
  3. [3] M. Balazard, Unimodalité de la distribution du nombre de diviseurs premiers d'un entier, Ann. Inst. Fourier (Grenoble) 40 (1990), 255-270. Zbl0711.11030
  4. [4] M. Balazard, H. Delange et J.-L. Nicolas, Sur le nombre de facteurs premiers des entiers, C. R. Acad. Sci. Paris Sér. I Math. 306 (1988), 511-514. Zbl0644.10032
  5. [5] M. Balazard, J.-L. Nicolas, C. Pomerance et G. Tenenbaum, Grandes déviations pour certaines fonctions arithmétiques, J. Number Theory 40 (1992), 146-164. Zbl0745.11041
  6. [6] M. Deléglise et J.-L. Nicolas, Sur les entiers n ≤ x dont le nombre de diviseurs est supérieur à logx, preprint. 
  7. [7] P. Erdős et J.-L. Nicolas, Sur la fonction: nombre de facteurs premiers de N, Enseign. Math. (2) 27 (1981), 3-27. 
  8. [8] H. Halberstam and K. F. Roth, Sequences, Vol. I, Oxford Univ. Press, Oxford, 1966. 
  9. [9] G. H. Hardy and S. Ramanujan, The normal number of prime factors of a number n, Quart. J. Math. 48 (1917), 76-92. Zbl46.0262.03
  10. [10] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 3rd ed., Oxford Univ. Press, Oxford, 1954. Zbl0058.03301
  11. [11] D. Hensley, The distribution of round numbers, Proc. London Math. Soc. (3) 54 (1987), 412-444. Zbl0588.10047
  12. [12] A. Hildebrand and G. Tenenbaum, On the number of prime factors of an integer, Duke Math. J. 56 (1988), 471-501. Zbl0655.10036
  13. [13] G. Kolesnik and E. G. Straus, On the distribution of integers with a given number of prime factors, Acta Arith. 37 (1980), 181-199. Zbl0446.10035
  14. [14] J. P. Kubilius, Probabilistic Methods in the Theory of Numbers, Transl. Math. Monographs 11, Amer. Math. Soc., Providence, R.I., 1964. Zbl0133.30203
  15. [15] J. P. Kubilius, On large deviations of additive arithmetic functions, Trudy Mat. Inst. Steklov. 128 (1972), 163-171 (= Proc. Steklov Inst. Math. 128 (1972), 191-201). 
  16. [16] K. K. Mardžanišvili, Estimation d'une somme arithmétique, C. R. (Dokl.) Acad. Sci. URSS (N.S.) 22 (1939), No. 7, 387-389. Zbl0021.20802
  17. [17] J.-L. Nicolas, Sur la distribution des nombres entiers ayant une quantité fixée de facteurs premiers, Acta Arith. 44 (1984), 191-200. Zbl0512.10034
  18. [18] K. K. Norton, On the number of restricted prime factors of an integer. I, Illinois J. Math. 20 (1976), 681-705. Zbl0329.10035
  19. [19] K. K. Norton, On the number of restricted prime factors of an integer. II, Acta Math. 143 (1979), 9-38. Zbl0417.10037
  20. [20] K. K. Norton, On the number of restricted prime factors of an integer. III, Enseign. Math. (2) 28 (1982), 31-52. Zbl0501.10046
  21. [21] K. K. Norton, Upper bounds for sums of powers of divisor functions, J. Number Theory 40 (1992), 60-85. Zbl0748.11046
  22. [22] C. Pomerance, On the distribution of round numbers, in: Number Theory (Ootacamund, 1984), Lecture Notes in Math. 1122, Springer, Berlin, 1985, 173-200. 
  23. [23] G. J. Rieger, Zum Teilerproblem von Atle Selberg, Math. Nachr. 30 (1965), 181-192. Zbl0131.04603
  24. [24] L. G. Sathe, On a problem of Hardy on the distribution of integers having a given number of prime factors, I, II, III, IV, J. Indian Math. Soc. (N.S.) 17 (1953), 63-141; 18 (1954), 27-81. 
  25. [25] A. Selberg, Note on a paper by L. G. Sathe, J. Indian Math. Soc. (N.S.) 18 (1954), 83-87. 
  26. [26] C. Spiro, Extensions of some formulae of A. Selberg, Internat. J. Math. Math. Sci. 8 (1985), 283-302. Zbl0573.10031
  27. [27] S. Wigert, Sur l'ordre de grandeur du nombre des diviseurs d'un entier, Ark. Mat. 3 (1907), no. 18, 1-9. 

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