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On a subgroup of the group of multiplicative arithmetic functions

Published online by Cambridge University Press:  09 April 2009

T. B. Carroll  and
A. A. Gioia
T. B. Carroll
Affiliation:
Western Michigan UniversityKalamazoo Michigan 49001, U.S.A.
A. A. Gioia
Affiliation:
Western Michigan UniversityKalamazoo Michigan 49001, U.S.A.
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An arithmetic function f is said to be multiplicative if f(1) = 1 and f(mn) = f(m)f(n) whenever (m, n) = 1, where (m, n) denotes as usual the greatest common divisor of m and n. Furthermore an arithmetic function is said to be linear (or completely multiplicative) if f(1) = 1 and f(mn) = f(m)f(n) for all positive integers m and n.The Dirichlet convolution of two arithmetic functions f and g is defined by for all n∈Z+. Recall that the set of all multiplicative functions, denoted by M, with this operation is an abelian group.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 3 , November 1975 , pp. 348 - 358
Copyright
Copyright © Australian Mathematical Society 1975

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