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Riemann zeta function

Functional equation of the Riemann zeta function

{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 $|t|$,
$$
|\chi(\sigma+it)|\asymp |t|^{1/2-\sigma}.
$$

Vertical-strip factor in the Riemann zeta functional equation

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 150 / 2 / c / Solution

Vertical-strip factor in the Riemann zeta functional equation

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Vertical-strip factor in the Riemann zeta functional equation

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