# Zeta function Re(s)=1 [duplicate]

Here I am considering the original zeta function (not the extended one)$$\zeta(s)=\sum_{n=1}^\infty \frac{1}{n^s}$$ When Re(s)>1, the Zeta function converges, and if Re(s)<1 it diverges.
• No, the series diverges whenever $\operatorname{Re} s = 1$. That's not totally easy to prove, though. – Daniel Fischer Jun 1 '16 at 13:38