The multinomial convolution sum of a generalized divisor function

Abstract

The main theorem of this article is to evaluate and express the multinomial convolution sum of the divisor function σr♯(n;N/4,N){\sigma }_{r}^{\sharp }\left(n;\hspace{0.33em}N\hspace{-0.08em}\text{/}\hspace{-0.08em}4,N) in as a simple form as possible, where N/4N\hspace{-0.08em}\text{/}\hspace{-0.08em}4 is an arbitrary odd positive integer. This generalizes previous result in combination with Cho and Kim, which is about the case N=4N=4. While obtaining our main theorem, we derive some generalizations of other identities to the case that we are dealing with.

Keywords

• divisor functions
• convolution sums
• 11a25
• 11y70