What is the convergence behaviour for $\sum_{n=0}^{\infty}\frac{1}{n^d}z^n$ with $z\in\mathbb{C},|z|=1$ and $0 < d \leq 1$?
Questions about the powerseries $\sum_{n=0}^{\infty}\frac{1}{n^d}z^n,d\in\mathbb{R},z\in\mathbb{C}$