 Vertical-strip factor in the Riemann zeta functional equation

ID: vertical-strip-factor-in-the-riemann-zeta-functional-equation

ζ (s) = χ (s) ζ (1 - s), χ (s) = 2^{s} π^{s - 1} sin (π s /2) Γ (1 - s),

the Stirling formula gives, uniformly on every fixed vertical strip and for large

∣ t ∣

∣ χ (σ + i t) ∣ ≍ ∣ t ∣^{1/2 - σ} .

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