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By the Vinogradov-Korobov estimate we have

$\left|\frac{\zeta^{(k)}}{\zeta} (1+it)\right| \le c_k Y^k(t)$ where $Y(t)= \ln^{2/3} (|t|+3) (\ln\ln (|t|+3))^{1//3}$ for some $c_k$.

I search the value of $c_k$ without the Riemann hypothesis or other hypothesis in the litterature.

Can you help me ?

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  • $\begingroup$ You may want to spend some time improving your question. $\endgroup$ Dec 4, 2015 at 22:44
  • $\begingroup$ Yes. Thank you. I search in the litterature. $\endgroup$
    – Claudeh5
    Dec 4, 2015 at 22:51

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