# Colin Defant

## Ranges of Divisor Functions

#### When/Where:

November 10, 2015, 3:00 — 3:50pm at LIT 368.

#### Abstract:

For any complex number $$c$$, let $$\sigma_c : N \rightarrow C$$ be the divisor function given by $$\sigma_c(n) =\displaystyle\sum_{d|n} d^c$$.

In this talk, I will discuss some of the history of divisor functions. I will then discuss some of my work concerning the ranges $$\sigma_c(N)$$. In particular, I will focus on some of the basic topological properties of $$\sigma_{-r}(N)$$ for $$r > 1$$.