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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The identical equation in $\psi$-products
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by V. Sitaramaiah and M. V. Subbarao PDF
Proc. Amer. Math. Soc. 124 (1996), 361-369 Request permission


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:
  • 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:
  • MathSciNet review: 1301528