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Some Results on the Distribution of the Values of Multiplicative Functions

G. Jogesh Babu
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 37, No. 3 (Jul., 1975), pp. 386-395
Published by: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25049998
Page Count: 10
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Some Results on the Distribution of the Values of Multiplicative Functions
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Abstract

Let g be a real-valued multiplicative function defined on the set of pairs of positive integers such that $g(2^{j},2^{k})=g(3^{j},3^{k})=1$ for all non-negative integers j and k. In this paper necessary and sufficient conditions are given for g to have a distribution. It is shown that if a multiplicative arithmetic function satisfies some local conditions, then it has a distribution. Some smoothness properties of the distributions of multiplicative arithmetic functions are also investigated.

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