Logarithmic operators and characterizations of completely multiplicative functions (Q1597747)

The authors show that the logarithmic operators in the ring of arithmetic functions given by \textit{D. Rearick} [Duke Math. J. 35, 761-766 (1968; Zbl 0169.37201)], \textit{L. Carlitz and M. V. Subbarao} [Duke Math. J. 40, 949-958 (1973; Zbl 0277.10007)] and \textit{H. Shapiro} [Introduction to the theory of numbers. Pure and Applied Mathematics. New York, Wiley (1983; Zbl 0515.10001)] are essentially the same. Some characterizations of completely multiplicative functions are derived as an application.