Some characterizations of specially multiplicative functions

Haukkanen, Pentti (2003)
 
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Haukkanen, Pentti
2003

International Journal of Mathematics and Mathematical Sciences 2003 37
2335-2344
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doi:10.1155/S0161171203301139
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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.
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