Abstract
One gives an application of Tauberian theorems to the problem of connection between the mean values of multiplicative functions for the cases when the argument runs through all natural numbers and all prime numbers, respectively.
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Literature cited
G. H. Hardy, Divergent Series, Clarendon Press, Oxford (1949).
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H. Delange, “Sur les fonctions arithmétiques multiplicatives,” Ann. Sci. École Norm. Sup.,78, 273–304 (1961).
B. V. Levin and A. S. Fainleib, “The application of certain integral equations to number theory problems,” Usp. Mat. Nauk,22, 119–198 (1967).
Additional information
The author dedicates this paper to A. I. Vinogradov on the occasion of his 50th birthday.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 91, pp. 145–157, 1979.
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Fainleib, A.S. Tauberian theorems and mean values of multiplicative functions. J Math Sci 17, 2181–2191 (1981). https://doi.org/10.1007/BF01567597
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DOI: https://doi.org/10.1007/BF01567597