Multiplicativity-preserving arithmetic power series

David Francis Rearick

Vol. 55 (1974), No. 1, 277–283

DOI: 10.2140/pjm.1974.55.277

Abstract

In the Dirichlet algebra of arithmetic functions let the operator A be represented by an arithmetic power series Af = Σa(F)f^F. A condition on the coefficients a(F) is derived which is necessary and sufficient for Af to be multiplicative whenever f is multiplicative.

Mathematical Subject Classification

Primary: 10A20

Milestones

Received: 20 March 1973

Published: 1 November 1974