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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

Gutti Jogesh Babu and
Paul Erdös
Gutti Jogesh Babu
Affiliation:
Department of Statistics, 219 Pond Laboratory Pennsylvania State University University Park, PA 16802, USA
Paul Erdös
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences Reàltanoda U 13-15 1053 Budapest V, Hungary
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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.

Keywords

10K2060F05

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 4 , 01 December 1989, pp. 441 - 445
Copyright
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