Colin Defant

Ranges of Divisor Functions


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


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 \(r > 1\).