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A Note on the Distribution Function of Additive Arithmetical Functions in Short Intervals
Published online by Cambridge University Press: 20 November 2018
Abstract
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Let f be an additive arithmetical function having a distribution F. For any sequence let
In this note, we determine the slowest growing function b so that Qn{b, f) tends weakly to F, for various f.
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- Copyright © Canadian Mathematical Society 1989
References
1.
Babu, G. J., Probabilistic methods in the theory of arithmetic functions, MacMillan Lectures in Mathematics, Series 2, Macmillan Company, New Delhi, 1978.Google Scholar
2.
Babu, G. J., On the mean values and distributions of arithmetic functions, Acta Arithmetica 40 (1981), 63–77.Google Scholar
3.
Babu, G. J., Distribution of the values of ω in short intervals, Acta Math. Acad. Sci. Hungar. 40 (1982), 135–137.Google Scholar
4.
Erdös, P., Note on consecutive abundant numbers, J. London Math. Soc, 10 (1935) 128–131.Google Scholar
5.
Halȧsz, G., Über die Mittelwerte Multiplicativer Zahlentheoretischer Funktionen, Acta Math. Acad. Sci. Hungar., 19 (1968) 365–403.Google Scholar
6.
Hildebrand, A., Multiplicative functions in short intervals, Can. J. Math., 39 (1987), 646–672.Google Scholar
7.
Indlekofer, K.-H., Limiting distributions of additive functions in short intervals, (1987) Preprint.Google Scholar
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