Some characterizations of specially multiplicative functions

Pentti Haukkanen

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-10

Abstract:

A multiplicative function f is said to be specially multiplicative if there is a completely multiplicative function f A such that f ( m ) f ( n ) = ∑ d | ( m , n ) f ( m n / d 2 ) f A ( 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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:515979

DOI: 10.1155/S0161171203301139

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