International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 37, Pages 2335-2344
doi:10.1155/S0161171203301139
Some characterizations of specially multiplicative functions
Department of Mathematics, Statistics and Philosophy, University of Tampere, FIN-33014, Finland
Received 10 January 2003
Copyright © 2003 Pentti Haukkanen. 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
A multiplicative function f is said to be specially multiplicative if there is a completely multiplicative function
fA such that f(m)f(n)=∑d|(m,n)f(mn/d2)fA(d) for all m and n. For example, the divisor functions and Ramanujan's τ-function are specially multiplicative functions. Some characterizations of specially multiplicative functions are given in the literature. In this paper, we provide
some further characterizations of specially multiplicative functions.