On the Dirichlet Convolution of Completely Additive Functions
Isao Kiuchi and Makoto Minamide
Department of Mathematical Sciences
Yamaguchi University
Yamaguchi 753-8512
Japan
Abstract:
Let k and l be non-negative integers.
For two completely additive functions f and g,
we consider various identities for the Dirichlet convolution of the kth
powers of f and the lth powers of g.
Furthermore, we derive some asymptotic formulas for sums of convolutions on the natural logarithms.
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Received April 23 2014;
revised version received May 15 2014; July 9 2014; July 20 2014;
July 31 2014.
Published in Journal of Integer Sequences, August 5 2014.
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