Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-15T05:48:57.266Z Has data issue: false hasContentIssue false
  • English
  • Français

Identities for Multiplicative Functions

Published online by Cambridge University Press:  20 November 2018

M. V. Subbarao  and
A. A. Gioia
M. V. Subbarao
Affiliation:
University of Alberta, University of Kerala and Texas Technological College
A. A. Gioia
Affiliation:
University of Alberta, University of Kerala and Texas Technological College
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Throughout this paper the arithmetic functions L(n) and w(n) denote respectively the number and product of the distinct prime divisors of the integer n > 1, with L(1) = 0 and w(1) = 1. Also let

We recall that an arithmetic function f(n) is said to be multiplicative if f(1) = 1 and f(mn) = f(m)f(n) whenever (m, n) = 1, where (m, n) denotes as usual the greatest common divisor of m and n.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 1 , April 1967 , pp. 65 - 73
Copyright
Copyright © Canadian Mathematical Society 1967

Footnotes

1

Partially supported by National Science Foundation Grant No. GP 1222.

2

This author's contribution formed a part of his Ph.D. thesis submitted to the University of Missouri in January, 1964.

References

1. Cohen, Eckford, Arithmetical functions associated with the unitary divisors of an integer. Math. Zeit., 74 (I960), pages 66-80,CrossRefGoogle Scholar
2. Cohen, Eckford, Unitary functions (mod r ). Duke Math. J., 28 (1966), pages 475 - 485.Google Scholar
3. Gioia, A. A., On an identity for multiplicative functions. Amer. Math. Monthly, 69 (1966), pages 988-991.CrossRefGoogle Scholar
4. Gioia, A. A., The K-product of arithmetic functions. Can. J.Math., 17 (1966), pages 970-976.Google Scholar
5. Gioia, A. A. and Subbarao, M. V., Generalized Dirichlet products of arithmetic functions (Abstract). Notices Amer. Math. Soc, 9 (1966), page 305.Google Scholar
6. Vaidyanathaswamy, R., The identical equation of the multiplicative functions. Bull. Amer. Math. Soc, 36 (1933), pages 762-772.Google Scholar
7. Vaidyanathaswamy, R., The theory of multiplicative arithmetic functions. Trans. Amer. Math. Soc, 33 (1933) pages 579-662.Google Scholar