Vertical-strip factor in the Riemann zeta functional equation
= Vertical-strip factor in the Riemann zeta functional equation
{c}
Writing
$$
\zeta(s)=\chi(s)\zeta(1-s),
\qquad
\chi(s)=2^s\pi^{s-1}\sin(\pi s/2)\Gamma(1-s),
$$
the <Stirling formula> gives, uniformly on every fixed vertical strip and for large $|t|$,
$$
|\chi(\sigma+it)|\asymp |t|^{1/2-\sigma}.
$$