partition theory

Question

I've read an article of Hardy and Ramanujan where it appears the expression $\sum_{\nu=2}^{\infty}e^{-s\nu^{r}}\sim \Gamma\left(\frac{1}{r}+1\right)s^{\frac{-1}{r}}$ when $s\to 0$. I've tried usual calculus techniques but haven't been able to figure it out. Could anybody give me a hint? Thanks