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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

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.

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

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