Geodesic
The joint distribution of multiplicative functions
Čebyševskij sbornik, Tome 10 (2009) no. 1, pp. 41-58.

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In the paper, the existence of a joint limit distribution for a real multiplicative and a complex-valued multiplicative functions is considered. For one class of multiplicative functions, the necessary and sufficient conditions for the existence of a limit distribution are obtained. 
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A. Laurinčikas. The joint distribution of multiplicative functions. Čebyševskij sbornik, Tome 10 (2009) no. 1, pp. 41-58. http://geodesic.mathdoc.fr/item/CHEB_2009_10_1_a3/

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