Generalizations of Dirichlet Convolution

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


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
$$ (f{*_K}g)(n) = \sum\limits_{{d\left| n \right.}} K (n,d)f(d)g(n/d)\quad {\text{for}}\,{\text{all}}\,{\text{n}} $$


Positive Integer Commutative Ring Basic Sequence Multiplicative Function Great Common Divisor 
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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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