Papers

The multinomial convolution sums of certain divisor functions

https://doi.org/10.1016/j.jmaa.2016.11.052

Research Fields산업수학전략연구부
Author Bumkyu Cho, Daeyeoul Kim*, Ho Park
JournalJournal of mathematical analysis and applications 448(2) (2017
Link https://doi.org/10.1016/j.jmaa.2016.11.052
Classification of papersSCI
KeywordDivisor functions; Convolution sums

In this article we first introduce some results about the binomial, trinomial, and quadrinomial convolution sums of certain divisor functions and then we provide an identity for the multinomial convolution sums of the divisor function

σ_{r}^{？} (n) : = \sum_{\begin{matrix} d | n \\ n / d \equiv 1 (4) \end{matrix}} d^{r} - {(- 1)}^{r} \sum_{\begin{matrix} d | n \\ n / d \equiv - 1 (4) \end{matrix}} d^{r}

σ_{r}^{？} (n) : = \sum_{\begin{matrix} d | n \\ n / d \equiv 1 (4) \end{matrix}} d^{r} - {(- 1)}^{r} \sum_{\begin{matrix} d | n \\ n / d \equiv - 1 (4) \end{matrix}} d^{r}