On Gaps in the Closures of Images of Divisor Functions

Niven Achenjang, Aaron Berger

Given a complex number $c$, define the divisor function ${\sigma }_c:\mathbb{N}\to \mathbb{C}$ by ${\sigma }_c(n)={\sum }_{d\mid n}{d}^c$. In this paper, we look at $\overline{{\sigma }_{-r}(\mathbb{N})}$, the top…