Geodesic
On the Dirichlet convolution of completely additive functions
Journal of integer sequences, Tome 17 (2014) no. 8
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 $k$th powers of $f$ and the $l$th powers of $g$. Furthermore, we derive some asymptotic formulas for sums of convolutions on the natural logarithms.
Classification : 11A25, 11P99
Keywords: completely additive function, Dirichlet convolution 
@article{JIS_2014__17_8_a3,
     author = {Kiuchi,  Isao and Minamide,  Makoto},
     title = {On the {Dirichlet} convolution of completely additive functions},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {8},
     zbl = {1358.11017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_8_a3/}
}
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Kiuchi,  Isao; Minamide,  Makoto. On the Dirichlet convolution of completely additive functions. Journal of integer sequences, Tome 17 (2014) no. 8. http://geodesic.mathdoc.fr/item/JIS_2014__17_8_a3/