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A class of additive arithmetic functions with asymptotically normal distribution

Published online by Cambridge University Press:  26 February 2010

P. D. T. A. Elliott
P. D. T. A. Elliott
Affiliation:
Department of Mathematics, Boulder, Colorado, U.S.A.
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Extract

Let f(n) be a real-valued additive arithmetic function. For each positive rational integer n set

For the duration of this paper we shall assume that as n → ∞ both

Type
Research Article
Information
Mathematika , Volume 20 , Issue 2 , December 1973 , pp. 144 - 154
Copyright
Copyright © University College London 1973

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References

1. Barban, M. B., “On a theorem of J. P. Kubilius”, Izv. Akad. Nauk. USSR. Ser. Fiz. Mat. Nauk., 1961 (5), 3–9.Google Scholar
2. Erdős, P. and Kac, M., “The Gaussian law of errors in the theory of additive number-theoretic functions”, Amer. J. Math., 62 (1940), 738–742.CrossRefGoogle Scholar
3. Esseen, C. G., “Fourier Analysis of distribution functions. A mathematical study of the Laplace- Gaussian law”, Ada Math., 77 (1945), 1–125.Google Scholar
4. Hálasz, G., “On the distribution of additive and the mean values of multiplicative arithmetic functions”, Studia Scient. Math. Hungar., 6 (1971), 211–233.Google Scholar
5. Kubilius, J., “A class of additive number-theoretic functions with asymptotically normal distribution”, Naucn. Trudy Fiz-Tehn. Inst. Akad. Nauk. Lit. SSSR, 2 (1956), 5–15.Google Scholar
6. Kubilius, J., Probabilistic methods in the theory of numbers (American Math. Soc. Translations, No. 11).Google Scholar