Author:
Carroll T. B.,Gioia A. A.
Abstract
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.
Publisher
Cambridge University Press (CUP)
Reference12 articles.
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