@article{bwmeta1.element.bwnjournal-article-aav68i3p219bwm,
author = {Karl K. Norton},
title = {On the frequencies of large values of divisor functions},
journal = {Acta Arithmetica},
volume = {68},
year = {1994},
pages = {219-244},
zbl = {0816.11047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav68i3p219bwm}
}
Karl K. Norton. On the frequencies of large values of divisor functions. Acta Arithmetica, Tome 68 (1994) pp. 219-244. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav68i3p219bwm/
[000] [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.
[001] [2] M. Balazard, Remarques sur un théorème de G. Halász et A. Sárközy, Bull. Soc. Math. France 117 (1989), 389-413.
[002] [3] M. Balazard, Unimodalité de la distribution du nombre de diviseurs premiers d'un entier, Ann. Inst. Fourier (Grenoble) 40 (1990), 255-270. | Zbl 0711.11030
[003] [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. | Zbl 0644.10032
[004] [5] M. Balazard, J.-L. Nicolas, C. Pomerance et G. Tenenbaum, Grandes déviations pour certaines fonctions arithmétiques, J. Number Theory 40 (1992), 146-164. | Zbl 0745.11041
[005] [6] M. Deléglise et J.-L. Nicolas, Sur les entiers n ≤ x dont le nombre de diviseurs est supérieur à logx, preprint.
[006] [7] P. Erdős et J.-L. Nicolas, Sur la fonction: nombre de facteurs premiers de N, Enseign. Math. (2) 27 (1981), 3-27.
[007] [8] H. Halberstam and K. F. Roth, Sequences, Vol. I, Oxford Univ. Press, Oxford, 1966.
[008] [9] G. H. Hardy and S. Ramanujan, The normal number of prime factors of a number n, Quart. J. Math. 48 (1917), 76-92. | Zbl 46.0262.03
[009] [10] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 3rd ed., Oxford Univ. Press, Oxford, 1954. | Zbl 0058.03301
[010] [11] D. Hensley, The distribution of round numbers, Proc. London Math. Soc. (3) 54 (1987), 412-444. | Zbl 0588.10047
[011] [12] A. Hildebrand and G. Tenenbaum, On the number of prime factors of an integer, Duke Math. J. 56 (1988), 471-501. | Zbl 0655.10036
[012] [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. | Zbl 0446.10035
[013] [14] J. P. Kubilius, Probabilistic Methods in the Theory of Numbers, Transl. Math. Monographs 11, Amer. Math. Soc., Providence, R.I., 1964. | Zbl 0133.30203
[014] [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).
[015] [16] K. K. Mardžanišvili, Estimation d'une somme arithmétique, C. R. (Dokl.) Acad. Sci. URSS (N.S.) 22 (1939), No. 7, 387-389. | Zbl 0021.20802
[016] [17] J.-L. Nicolas, Sur la distribution des nombres entiers ayant une quantité fixée de facteurs premiers, Acta Arith. 44 (1984), 191-200. | Zbl 0512.10034
[017] [18] K. K. Norton, On the number of restricted prime factors of an integer. I, Illinois J. Math. 20 (1976), 681-705. | Zbl 0329.10035
[018] [19] K. K. Norton, On the number of restricted prime factors of an integer. II, Acta Math. 143 (1979), 9-38. | Zbl 0417.10037
[019] [20] K. K. Norton, On the number of restricted prime factors of an integer. III, Enseign. Math. (2) 28 (1982), 31-52. | Zbl 0501.10046
[020] [21] K. K. Norton, Upper bounds for sums of powers of divisor functions, J. Number Theory 40 (1992), 60-85. | Zbl 0748.11046
[021] [22] C. Pomerance, On the distribution of round numbers, in: Number Theory (Ootacamund, 1984), Lecture Notes in Math. 1122, Springer, Berlin, 1985, 173-200.
[022] [23] G. J. Rieger, Zum Teilerproblem von Atle Selberg, Math. Nachr. 30 (1965), 181-192. | Zbl 0131.04603
[023] [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.
[024] [25] A. Selberg, Note on a paper by L. G. Sathe, J. Indian Math. Soc. (N.S.) 18 (1954), 83-87.
[025] [26] C. Spiro, Extensions of some formulae of A. Selberg, Internat. J. Math. Math. Sci. 8 (1985), 283-302. | Zbl 0573.10031
[026] [27] S. Wigert, Sur l'ordre de grandeur du nombre des diviseurs d'un entier, Ark. Mat. 3 (1907), no. 18, 1-9.