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Arithmetic Functions

  • M. Ram Murty
Part of the Graduate Texts in Mathematics book series (GTM, volume 206)

Abstract

An arithmetic function f is a complex-valued function defined on the natural numbers. Such an f is called an additive function if
$$ f(mn) = f(m) + f(n) $$
(1.1)
whenever m and n are coprime. If (1.1) holds for all m, n, then f is called completely additive. A multiplicative function is an arithmetic function f satisfying f(l) = 1 and
$$ f(mn) = f(m)f(n) $$
(1.2)
whenever m and n are coprime. If (1.2) holds for all m, n, then f is called completely multiplicative.

Keywords

Prime Number Prime Divisor Inversion Formula Multiplicative Function Average Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • M. Ram Murty
    • 1
  1. 1.Department of MathematicsQueen’s UniversityKingstonCanada

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