Originally Posted by

**TheFinalPush** Hi,

I'm currently looking at the Riemann zeta function (r.z.f), particularly it's domain. I know we can show it is holomorphic in Re(z) > 1 and that we can see it has a singularity at 1 by rewriting its formula however, after this I get a bit confused.

Before the analytic continuation of the r.z.f, is it well defined for all the complex plane apart from 1?

Do we consider the analytic continuation of the r.z.f to make it well defined for all the complex plane or to show that it is meromorphic in Re(z) > 0 or both or none of these?

Thanks