Geodesic
On an arithmetic convolution
Journal of integer sequences, Tome 17 (2014) no. 6
The Cauchy-type product of two arithmetic functions $f$ and $g$ on nonnegative integers is defined by $(f \bullet g)(k) := \Sigma _{m=0}^{k} C(k, m) f(m)g(k-m)$. We explore some algebraic properties of the aforementioned convolution, which is a fundamental characteristic of the identities involving the Bernoulli numbers, the Bernoulli polynomials, the power sums, the sums of products, and so forth.
Classification : 11A25, 11B68, 05A10, 11B65
Keywords: Cauchy product, Cauchy-type product, Dirichlet convolution, arithmetic function, Bernoulli number, torsion-free group, Bernoulli polynomial, power sum 
@article{JIS_2014__17_6_a4,
     author = {Singh,  Jitender},
     title = {On an arithmetic convolution},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {6},
     zbl = {1317.11012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_6_a4/}
}
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Singh,  Jitender. On an arithmetic convolution. Journal of integer sequences, Tome 17 (2014) no. 6. http://geodesic.mathdoc.fr/item/JIS_2014__17_6_a4/