On additive functions whose limiting distributions possess a finite mean and variance

P. D. T. A. Elliott

Vol. 48 (1973), No. 1, 47–55

DOI: 10.2140/pjm.1973.48.47

Abstract

In this paper two characterizations are given of those additive arithmetic functions which possess a limiting distribution with a finite mean and variance. It turns out that the study of such functions fits naturally within the framework of the theory of Lambert series.

Mathematical Subject Classification

Primary: 10K20

Milestones

Received: 22 May 1972

Published: 1 September 1973