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We establish lower bounds for the discrete 2 k th moment of the derivative of the Riemann zeta function at nontrivial zeros for allk  &lt;  0   $k&amp;lt;0$    under the Riemann hypothesis and the assumption that all zeros ofζ  (  s  )   $\zeta (s)$    are simple.

Lower bounds for negative moments of ζ ′ ( ρ ) $\zeta ^{\prime }(\rho )$