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**raheel88** Consider the Von Mangoldt explicit formula, namely,

$\displaystyle \Psi (x) = x - \sum \frac{x^\rho}{\rho} + O (1)$

How can I prove that, assuming the Riemann Hypothesis to be true, then,

$\displaystyle \frac{\Psi (x) - x}{\sqrt x} = -2\sum \frac{sin(\gamma_n t)}{\gamma}$

where $\displaystyle \gamma_i$ is the imaginary part of the i-th non-trivial zeta zero.

I've had a decent stab at it but I get stuck in trying to manipulate the sum once I've divided by $\displaystyle \sqrt x$

Thanks in advance!