On an analogue of completely multiplicative functions.

Haukkanen, P.; Ruokonen, P.

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On a class of $ψ$ -convolutions characterized by the identical equation

Jean-Louis Nicolas, Varanasi Sitaramaiah (2002)

Journal de théorie des nombres de Bordeaux

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The identical equation for multiplicative functions established by R. Vaidyanathaswamy in the case of Dirichlet convolution in 1931 has been generalized to multiplicativity preserving $ψ$ -convolutions satisfying certain conditions (cf. [7]) which can be called as Lehmer-Narkiewicz convolutions for some reasons. In this paper we prove the converse.