Arithmetical function characterizations and identities induced through equivalence relations

Temba Shonhiwa
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 13, 2007, Number 3, Page 1—19
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Authors and affiliations

Temba Shonhiwa
School of Mathematics, University of the Witwatersrand
P. Bag 3, Wits 2050, South Africa


Let A denote the set of arithmetic functions and ∗ Dirichlet convolution. The paper presents and alternative approach to the study of arithmetic functions by introducing a homomorphism between the subgroup <U, ∗> of the group of units in <A, ∗> and the quotient ring induces through an equivalence relation. The same notion is extended to the case of unitary convolution.


  • Dirichlet and unitary convolution
  • Functional equation
  • Multiplicative and com­pletely multiplicative functions
  • Equivalence relation
  • Homomorphism

AMS Classification

  • 11A25


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Cite this paper

Shonhiwa, T. (2007). Arithmetical function characterizations and identities induced through equivalence relations. Notes on Number Theory and Discrete Mathematics, 13(3), 1-19.

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