The identical equation in $\psi$-products

Authors:
V. Sitaramaiah and M. V. Subbarao

Journal:
Proc. Amer. Math. Soc. **124** (1996), 361-369

MSC (1991):
Primary 11A25

DOI:
https://doi.org/10.1090/S0002-9939-96-03104-8

MathSciNet review:
1301528

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Abstract | References | Similar Articles | Additional Information

Abstract: In Bull. Amer. Math. Soc. **36** (1930), 762–772, R. Vaidyanatha- swamy established a remarkable identity valid for any multiplicative arithmetic function and involving Dirichlet convolution. D. H. Lehmer (Trans. Amer. Math. Soc. **33** (1931), 945–952) introduced a very general class of arithmetical convolutions, called $\psi$-products, which include the well-known Dirichlet products, Eckford Cohen’s unitary convolutions, and in fact Narkiewicz’s so-called regular $A$-convolutions. In this paper, we establish an identical equation valid for multiplicative arithmetic functions and Lehmer’s $\psi$-convolutions which yields, as special cases, all known identical equations valid for the Dirichlet and unitary convolutions, besides establishing identical equations for several new convolutions.

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Additional Information

**V. Sitaramaiah**

Affiliation:
Department of Mathematics, Pondicherry Engineering College, Pillaichavady, Pondicherry 605104, India

**M. V. Subbarao**

Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Email:
m.v.subbarao@ualberta.ca

Keywords:
Multiplicative arithmetic functions,
Lehmer product,
identical equation

Received by editor(s):
April 4, 1994

Received by editor(s) in revised form:
August 20, 1994

Additional Notes:
The second author was partly supported by an NSERC grant

Communicated by:
William W. Adams

Article copyright:
© Copyright 1996
American Mathematical Society