Vol. 41, No. 2, 1972

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Arithmetical properties of generalized Ramanujan sums

Tom M. (Mike) Apostol

Vol. 41 (1972), No. 2, 281–293
Abstract

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

            ∑
Sf,g(m,k) =      f(d)g(k∕d),
d|(m.k)
(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
Authors
Tom M. (Mike) Apostol