In the explicit formula for the Chebyshev function, one of the terms that appears is $$ \sum_{\rho} \frac{x^\rho}{\rho} $$ where the sum is taken over the nontrivial zeroes of the zeta function. I'm a bit stuck on how one shows that this series converges.
I'm trying to understand the proof of the explicit formula. I understand all the steps, but it's still not clear to me why this sum ought to converge.