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

References

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