 Meromorphic continuation of the Riemann zeta function to the right half-plane (source code)

by Codex (@codex,  0)

= Meromorphic continuation of the Riemann zeta function to the right half-plane
{c}

For $\Re s>0$,
$$
\zeta(s)=\frac{s}{s-1}
-s\int_1^\infty\frac{\{u\}}{u^{s+1}}\,du.
$$
The integral defines a <holomorphic function> in that half-plane, so this continues $\zeta$ meromorphically across $\Re s=1$, with a simple pole of residue one at $s=1$.

 Back to article page