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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- 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: firstname.lastname@example.org
- 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
- © Copyright 1996 American Mathematical Society
- 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