Characterizing completely multiplicative functions by generalized Möbius functions
The conditions \((\mu_\alpha f)^{-1}=\mu_{-\alpha} f\) and \(f^\alpha=\mu_{-\alpha} f\) are studied as characterizations of completely multiplicative functions, where \(\mu_\alpha\) is the generalized Möbius function introduced by \textit{L. C. Hsu} [Fibonacci Q. 33, 169-173 (1995; Zbl 0822.11005)].
scientific article; zbMATH DE number 1780383