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 Laohakosol,1 Nittiya Pabhapote,2 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

Received 23 March 2001; Revised 15 August 2001

Copyright © 2002 Vichian Laohakosol et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.