Can someone help me why does this equation holds:
$\sum_{\rho}(1/2 + t -\rho)^{-s}= e^{i\pi s/2}\sum_{k=1}^{\infty}(\tau_k+it)^{-s}+e^{-i\pi s/2}\sum_{k=1}^{\infty}(\tau_k-it)^{-s}$ for $\rho=1/2 \pm i\tau_k$?
I tried expanding in the Taylor series function $e^{i\pi s/2}$ or as $e^{i\pi s/2}=\cos (\pi s/2) +i \sin(\pi s/2)$, but I get stacked.