Characterizing completely multiplicative functions by generalized Möbius functions - Vichian Laohakosol; Nittiya Pabhapote; Nalinee Wechwiriyakul (International Journal of Mathematics and Mathematical Sciences)
Using the generalized Möbius functions, μα, first introduced by Hsu (1995), two characterizations of completely multiplicative functions are given; save a minor condition they read (μαf)−1=μ−αf and fα=μ−αf.