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
Full paper (PDF, 6018Kb

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Authors and affiliations

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

Abstract

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.

Keywords

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

AMS Classification

• 11A25

References

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