I am wondering whether one could find Riemann zeta zeros iteratively by using relationships such as this one:
$$\rho _1=\lim_{s\to 1} \, \frac{\zeta (s) \zeta \left(s \cdot \rho _1\right)}{\zeta '(\rho _1)}$$
where $\rho _1 \approx 0.5 + 14.1347i$ is the first zeta zero.
Are there better relationships like Newton iteration or something like that?
The relation above that I tried to use diverges when trying to iterate it.