1.(a) Show that zeta(s) has zeros of order 1 at the even negative integers.
1.(b) Show that the only other zeros are such that $0\leq Re(s)\leq 1$.
1(c) Prove that the zeros of (b) actually have $Re(s)=1/2$. [You can ask the professor teaching the course for a hint on that one].
Source: Complex Analysis by Serge Lang