Journal of Integer Sequences, Vol. 17 (2014), Article 14.8.7

On the Dirichlet Convolution of Completely Additive Functions

Isao Kiuchi and Makoto Minamide
Department of Mathematical Sciences
Yamaguchi University
Yamaguchi 753-8512


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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