Abstract:
In this talk, we introduce the Euler function $\varphi(x)=\prod_{n=1}^{\infty}(1-x^n)$. This function has some unusual properties with applications in combinatorics and number theory. We will also discuss identities related to this function attributed to Gauss and Jacobi. This talk will be almost entirely self contained, but the notion of an integer partition will be helpful.