How can I prove that $$ -\frac{\zeta'(z)}{\zeta(z)}-\frac{1}{z-1}=O(|z|^{M})\quad\text{for }\Re(z)\geq1 $$ for $M$ constant large enough? $\zeta(s)$ is Riemann zeta function.
2026-04-11 22:41:21.1775947281
growth condition for Zeta function
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