Bulletin of the American Mathematical Society

Author(s): P. D. T. A. Elliott
Journal: Bull. Amer. Math. Soc. 16 (1987), 179-223.
MSC (1985): Primary 11K65, 11N37, 47B99
MathSciNet review: 876958
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1.: E. Bombieri, On the large sieve, Mathematika 12 (1965), 201-225. MR 197425
2.: H. Davenport, Multiplicative number theory (2nd ed.), Graduate Texts in Math., vol. 74, Springer-Verlag, New York, Berlin, Heidelberg, 1980. MR 606931
3.: F. Dress and B. Volkmann, Ensembles d'unicité pour les fonctions arithmétiques additives ou multiplicatives, C. R. Acad. Sci. Paris, Sér. A 287 (1978), 43-46. MR 491439
4.: P. D. T. A. Elliott, On inequalities of large sieve type, Acta Arith. 18 (1971), 405-422. MR 286774
5.: P. D. T. A. Elliott, On connections between the Turán-Kubilius inequality and the Large Sieve: Some applications, Proc. Sympos. Pure Math., vol. 24, Amer. Math. Soc., Providence, R. I., 1973, pp. 77-82. MR 344215
6.: P. D. T. A. Elliott, On the limiting distribution of additive arithmetic functions, Acta Math. 132 (1974), 53-75. MR 325562
7.: P. D. T. A. Elliott, The law of large numbers for additive arithmetic functions, Math. Proc. Cambridge Philos. Soc. 78 (1975), 33-71. MR 387229
8.: P. D. T. A. Elliott, General asymptotic distributions for additive arithmetic functions, Math. Proc. Cambridge Philos. Soc. 79 (1976), 43-54. MR 392892
9.: P. D. T. A. Elliott, The Turán-Kubilius inequality, Proc. Amer. Math. Soc. 65 (1977), 8-10. MR 447163
10.: P. D. T. A. Elliott, On the difference of additive functions, Mathematika 24 (1977), 153-165. MR 472734
11.: P. D. T. A. Elliott, Probabilistic number theory. I, II, Grundlehren math. Wiss., vols. 239, 240, Springer-Verlag, New York, Heidelberg, Berlin, 1979/80. MR 551361
12.: P. D. T. A. Elliott, High-power analogues of the Turán-Kubilius inequality and an application to number theory, Canad. J. Math. 32 (1980), 893-907. MR 590654
13.: P. D. T. A. Elliott, Arithmetic functions and integer products, Grundlehren math. Wiss., vol. 272, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1984/85. MR 766558
14.: P. D. T. A. Elliott, Cauchy's functional equation in the mean, Adv. in Math. 51 (3) (1984), 253-257. MR 740585
15.: P. D. T. A. Elliott, The exponential function characterized by an approximate functional equation, Illinois J. Math. 26 (1982), 503-518. MR 658460
16.: P. D. T. A. Elliott and C. Ryavec, The distribution of the values of additive arithmetical functions, Acta Math. 126 (1971), 143-164. MR 277491
17.: P. Erdős, On the distribution function of additive functions, Ann. of Math. (2) 47 (1946), 1-20. MR 15424
18.: P. Erdős and M. Kac, On the Gaussian law of errors in the theory of additive functions, Proc. Nat. Acad. Sci. U.S.A. 25 (1939), 206-207.
19.: P. Erdős and M. Kac, The Gaussian law of errors in the theory of additive number-theoretic functions, Amer. J. Math. 62 (1940), 738-742. MR 2374
20.: G. Halász, Über die Mittelwerte multiplikativer zahlentheoretischer Funktionen, Acta Math. Acad. Sci. Hungar. 19 (1968), 365-403. MR 230694
21.: G. H. Hardy and S. Ramanujan, The normal number of prime factors of a number n, Quart. J. Math. (Oxford) 48 (1917), 76-92.
22.: A. Hildebrand, Sur les moments d'une fonction additive, Ann. Inst. Fourier 33 (1983), 1-22. MR 723945
23.: A. Hildebrand, An asymptotic formula for the variance of an additive function, Math. Z. 183 (1983), 145-170. MR 704101
24.: I. Kátai, On a problem of P. Erdős, J. Number Theory 2 (1970), 1-6. MR 250991
25.: J. P. Kubilius, Probabilistic methods in the theory of numbers, Uspekhi Mat. Nauk (N.S.) 11 (1956), 2(68), 31-66; Amer. Math. Soc. Transl., Vol. 19 (1962), 47-85. MR 131415
26.: J. P. Kubilius, Probabilistic methods in the theory of numbers, Trans. Math. Monographs, vol. 11, Amer. Math. Soc., Providence, R. I., 1964. MR 160745
27.: J. P. Kubilius, On an inequality for additive arithmetic functions, Acta Arithmetica 27 (1975), 371-383. MR 366859
28.: J. P. Kubilius, On the estimation of the second central moment for strongly additive arithmetic functions, Liet. Mat. Rinkinys = Litovsk Mat. Sbornik 23 (1983), (1) 122-123. MR 705734
29.: J. P. Kubilius, On the estimate of the second central moment for arbitrary arithmetic functions, Liet. Mat. Rinkinys = Litovsk Mat. Sbornik 23 (1983), (2) 110-117. MR 706013
30.: S. Lang, Algebra, Addison-Wesley, Reading, Mass., 1965. MR 197234
31.: B. V. Levin and N. M. Timofeev, An analytic method in the probabilistic theory of numbers, Uchen. Zap. Vladimirskovo Gos. Ped. Inst. Mat. 57 (2) (1971), 57-150. MR 302596
32.: J. Meyer, Ensembles d'unicité pour les fonctions additives. Étude analogue dans le cas des fonctions multiplicatives, Journées de Theorie Analytique et Elémentaire des Nombres, (Orsay, 2 et 3 Juin, 1980), Publ. Math. Orsay, pp. 50-66. MR 610263
33.: K. Prachar, Primzahlverteilung, Grundlehren math. Wiss., vol. 91, Springer-Verlag, Berlin, 1957. MR 516660
34.: E. D. Rainville, Special functions, Macmillan, New York, 1960. MR 107725
35.: I. Z. Ruzsa, General multiplicative functions, Acta Arith. 32 (1977), 313-347. MR 432572
36.: I. Z. Ruzsa, On the concentration of additive functions, Acta Math. Acad. Sci. Hungar. 36 (1980), 215-232. MR 612193
37.: I. Z. Ruzsa, On the variance of additive functions, Turán Memorial Volume of the J. Bolyai Math. Soc., Hungary.
38.: I. Z. Ruzsa, Generalized moments of additive functions, J. Number Theory, 18 (1984), 27-33. MR 734434
39.: P. Turán, On a theorem of Hardy and Ramanujan, J. London Math. Soc. 9 (1934), 274-276.
40.: P. Turán, Über einige Verallgemeinerungen eines Satzes von Hardy and Ramanujan, J. London Math. Soc. 11 (1936), 125-133.
41.: E. Wirsing, A characterization of log n as an additive arithmetic function, Symposia Mathematica IV, 45-57, Academic Press, London and New York, 1970. MR 271049
42.: E. Wirsing, Characterization of the logarithm as an additive function, Proc. Sympos. Pure Math., vol. 20, Amer. Math. Soc., Providence, R. I., 1971, pp. 375-381. MR 412129
43.: D. Wolke, Bemerkungen über Eindeutigkeitsmengen additiver Funktionen, Elem. Math. 33 (1978), 14-16. MR 463096
44.: K. Yosida, Functional analysis, Grundlehren math. Wiss., vol. 123, 3rd éd., Springer-Verlag, New York, Berlin, Heidelberg, 1971.

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