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Generalizations of Dirichlet Convolution

  • Paul J. McCarthy
Part of the Universitext book series (UTX)

Abstract

Let K be a complex-valued function on the set of all ordered pairs <n,d> where n is a positive integer and d is a divisor of n. If f and g are arithmetical functions, their K-convolution, f *K g, is defined by
$$ (f{*_K}g)(n) = \sum\limits_{{d\left| n \right.}} K (n,d)f(d)g(n/d)\quad {\text{for}}\,{\text{all}}\,{\text{n}} $$

Keywords

Positive Integer Commutative Ring Basic Sequence Multiplicative Function Great Common Divisor 
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-Verlag New York Inc. 1986

Authors and Affiliations

  • Paul J. McCarthy
    • 1
  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA

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