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The law of large numbers for additive arithmetic functions

Published online by Cambridge University Press:  24 October 2008

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

Let f(n) be a real-valued additive arithmetic function, that is to say, that f(ab) = f(a) + f(b) for each pair of coprime integers a and b. Let α(x) and β(x) > 0 be real-valued functions, defined for x ≥ 2. In this paper, we study the frequencies

We shall establish necessary and sufficient conditions, subject to rather weak growth conditions upon β(x) alone, in order that these frequencies converge to the improper law, in other words, that f(n) obey a form of the weak law of large numbers.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 1 , July 1975 , pp. 33 - 71
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

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