Arithmetical properties of generalized Ramanujan sums

Tom M. (Mike) Apostol

Vol. 41 (1972), No. 2, 281–293

DOI: 10.2140/pjm.1972.41.281

Abstract

The sums studied in this paper are defined as follows. For any two arithmetical functions f and g, let

(1)

where the sum extends over the divisors of the greatest common divisor (m,k) of the positive integers m and k. It should be noted that m and k do not enter symmetrically in (1) unless g is constant.

Mathematical Subject Classification

Primary: 10H25

Milestones

Received: 4 February 1971

Published: 1 May 1972