On an arithmetic convolution

Abstract

The Cauchy-type product of two arithmetic functions $f$ and $g$ on nonnegative integers is defined as $(f\bullet g)(k):={\sum }_{m=0}^k\left(\genfrac{}{}{0ex}{}{k}{m}\right)f(m)g(k-m)$. 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, henceforth.

10 pages

References in corpus (1)

• On the binomial convolution of arithmetical functions