On an Analogue of Completely Multiplicative Functions

Pentti Haukkanen and Pia Ruokonen

Abstract: We introduce exponentially $A$-multiplicative functions which serve as an analogue of completely multiplicative functions in the setting of exponential $A$-convolu\-tion, where $A$ is Narkiewicz's regular convolution. We show that exponentially $A$-multi\-plicative functions under exponential $A$-convolution possess properties similar to the familiar properties of completely multiplicative functions under the Dirichlet convolution.

Keywords: Exponential convolution; Narkiewicz's regular convolution; completely multiplicative functions; characterizations; functional equations.

Classification (MSC2000): 11A25

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