Product Equation for Riemann Zeta Function/Warning

Warning
The sum $\ds \sum_\rho \frac 1 {\size \rho}$ diverges, so we must be careful of the order in which we take the terms.

By the functional equation for $\zeta$, the zeroes occur in complex conjugate pairs, and:


 * $\ds \frac 1 \rho + \frac 1 {\overline \rho} = \frac {2 \map \Re \rho} {\size \rho^2} \le \frac 2 {\size \rho^2}$

and we see by the corollary to Zeros of Functions of Finite Order that a sum of such terms does converge.