Elementary evaluation of certain convolution sums involving divisor functions.(English)Zbl 1062.11005

Bennett, M. A. (ed.) et al., Number theory for the millennium II. Proceedings of the millennial conference on number theory, Urbana-Champaign, IL, USA, May 21–26, 2000. Natick, MA: A K Peters (ISBN 1-56881-146-2/hbk). 229-274 (2002).
Let $$\sigma_m(n)= \sum_{d| n} d^m$$, where the integer $$m\geq 0$$. The authors begin by deriving an arithmetic identity that generalizes a formula of Liouville. This new identity enables them to prove a variety of convolution-type identities concerning $$\sigma_m(n)$$. Most of these convolution-type identities had been proven earlier using different methods by other researchers.
For the entire collection see [Zbl 1002.00006].

MSC:

 11A25 Arithmetic functions; related numbers; inversion formulas 11N37 Asymptotic results on arithmetic functions

Keywords:

divisor functions