Vol. 44, No. 1, 1973

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Groups of arithmetic functions under Dirichlet convolution

Roy W. Ryden

Vol. 44 (1973), No. 1, 355–360
Abstract

If f is an arithmetic function, let T(f) = {(a,b)|f(ab) = f(a)f(b)}. If S is a set of pairs of positive integers, let f M(S) if T(f) S. In this paper we determine all sets S such that M(S) is a group under Dirichlet convolution.

Mathematical Subject Classification
Primary: 10A20
Milestones
Received: 1 September 1971
Published: 1 January 1973
Authors
Roy W. Ryden