Along this path he first shows that his ζ-function has a
meromorphic continuation to C. Secondly, he proposes what has remained
as perhaps the most-famous unsolved problem of our day:
The Riemann Hypothesis: ζ(s) ≠ 0 for Re (s) > 1/2.
The Riemann Hypothesis: zeta(s) 不等於零,其中Re(s)大於1/2.
Our role here is not so much to focus on the zeroes of zeta(s), but in
some sense rather on its poles. In particular, our emphasis will be on
explaining how we know that zeta(s) extends meromorphically to the
entire complex plane.