Convolutions of arithmetic functions over cohesive basic sequences

Anthony Alfred Gioia and Donald Goldsmith

Vol. 38 (1971), No. 2, 391–399

DOI: 10.2140/pjm.1971.38.391

Abstract

Necessary and sufficient conditions are given for the generalized convolution of two arithmetic functions which are units with respect to a basic sequence ℬ to be again a unit on ℬ. These conditions are then investigated from function-theoretic and combinatorial points of view.

Mathematical Subject Classification

Primary: 10A20

Milestones

Received: 31 March 1970

Published: 1 August 1971