Geodesic
Tauberian theorems and mean values of multiplicative functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 2, Tome 91 (1979), pp. 145-157

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Tauberian theorems are applied to the problem of connection between the mean values of multiplicative functions for the cases when the argument runs over all natural numbers and all prime numbers. 
@article{ZNSL_1979_91_a10,
     author = {A. S. Fainleib},
     title = {Tauberian theorems and mean values of multiplicative functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {145--157},
     publisher = {mathdoc},
     volume = {91},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_91_a10/}
}
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A. S. Fainleib. Tauberian theorems and mean values of multiplicative functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 2, Tome 91 (1979), pp. 145-157. http://geodesic.mathdoc.fr/item/ZNSL_1979_91_a10/