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Some characterizations of specially multiplicative functions

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  • Pentti Haukkanen

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.

Suggested Citation

  • Pentti Haukkanen, 2003. "Some characterizations of specially multiplicative functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:515979
    DOI: 10.1155/S0161171203301139
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