Recent progress in probabilistic number theory

Journées arithmétiques de Besançon, Astérisque, no. 147-148 (1987), 12 p.

Zbl 0624.10045

@incollection{AST_1987__147-148__95_0,
     author = {Hildebrand, Adolf},
     title = {Recent progress in probabilistic number theory},
     booktitle = {Journ\'ees arithm\'etiques de Besan\c con},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {147-148},
     year = {1987},
     zbl = {0624.10045},
     language = {en},
     url = {www.numdam.org/item/AST_1987__147-148__95_0/}
}

Hildebrand, Adolf. Recent progress in probabilistic number theory, dans Journées arithmétiques de Besançon, Astérisque, no. 147-148 (1987), 12 p. http://www.numdam.org/item/AST_1987__147-148__95_0/

Bibliographie

[1] H. Delange, Sur les fonctions arithmétiques multiplicatives. Ann. Sci. Ec. Norm. Sup. 78 (1961), 273-304. | Article | EuDML 81772 | Zbl 0234.10043

[2] H. Delange, Théorie probabiliste des nombres. Astérisque 94 (1982), 31-42. | Zbl 0499.10055

[3] P. D. T. A. Elliott, Probabilistic Number Theory I, II. Springer. New York 1979, 1980. | Zbl 0431.10029

[4] P. D. T. A. Elliott, Arithmetic Functions and Integer Products. Springer. New York 1985. | Article | Zbl 0559.10032

[5] P. Erdös, On the distribution of additive functions. Ann. Math. 47 (1946), 1-20. | Article | Zbl 0061.07902

[6] P. Erdös 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. | Article | JFM 65.0164.02

[7] G. Halász, Über Mittelwerte zahlentheoretischer Funktionen. Acta Math. Acad. Sci. Hung. 19 (1968), 365-403. | Article | Zbl 0165.05804

[8] G. H. Hardy and S. Ramanujan, The normal number of prime factors of a number n. Quart. J. Math. (Oxford) 48 (1917), 76-92. | JFM 46.0262.03

[9] A. Hildebrand, On Wirsing's mean value theorem for multiplicative functions. Bull. London Math. Soc., to appear. | Zbl 0564.10048

[10] A. Hildebrand, Multiplicative functions in short intervals. Preprint. | Article | Zbl 0618.10040

[11] I. Katai, Some results and problems in the theory of additive functions. Acta Sci. Math. (Szeged) 30 (1969), 305-311. | Zbl 0186.35901

[12] I. Katai, On a problem of P. Erdös. J. Number Theory 2 (1970), 1-6. | Article | Zbl 0188.34201

[13] I. Katai, On random multiplicative functions. Acta Sci. Math. (Szeged) 33 (1972), 81-89. | Zbl 0244.10049

[14] J. Kubilius, Probabilistic Methods in the Theory of Numbers. Am. Math. Soc. Transl. of Math. Monographs 11. Providence, 1964. | Zbl 0133.30203

[15] J. Kubilius, Estimating the second central moment for arbitrary additive functions. Litovskii Mat. Sbornik 23 (1983) (2), 110-117. | Zbl 0531.10054

[16] I. Z. Ruzsa, On the variance of an additive function. In: P. Erdös (Ed.), Studies in Pure Mathematics, to the memory of Paul Turán. Akademiai Kiado. Budapest 1983. | Article | Zbl 0519.10045

[17] H. N. Shapiro, Distribution functions of additive arithmetic functions. Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 426-430. | Article | Zbl 0071.04202

[18] P. Turán, On a theorem of Hardy and Ramanujan. J. London Math. Soc. 9 (1934), 274-276. | Article | JFM 60.0145.02 | Zbl 0010.10401

[19] E. Wirsing, Das asymptotische Verhalten von Summen über multiplikative Funktionen II. Acta Math. Sci. Hung. 18 (1967), 411-467. | Article | Zbl 0165.05901

[20] E. Wirsing, Characterization of the logarithm as an additive function. Am. Math. Soc. Proc. Symp. Pure Math. XX (1971), 375-381. | Article | Zbl 0223.10035

[21] E. Wirsing, Additive and completely additive functions with restricted growth. In: Recent Progress in Analytic Number Theory, Proc. of Symposium, Durham 1979. Vol. 2, 231-280. Academic Press, London 1981. | Zbl 0462.10037

[22] E. Wirsing, Growth and differences of additive functions. Topics in Classical Number Theory. Colloquia Mathematica Societas Janos Bolyai 34, Budapest 1981, 1651-1661. | Zbl 0546.10048