International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 11, Pages 633-639
doi:10.1155/S0161171202012498
Characterizing completely multiplicative functions by generalized Möbius functions
Vichian Laohakosol1
, Nittiya Pabhapote2
and Nalinee Wechwiriyakul2
1Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand
2Department of Mathematics, Faculty of Science, The University of the Thai Chamber of Commerce, Bangkok 10400, Thailand
Abstract
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.