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Let $C(N)=\sum_{1<n\le N}{n^{-it}}$.

Vinogradov- Korobov estimate is

$$|C(N)| \le KN\exp\left(-\gamma \frac{\ln^3 N}{\ln^2 t}\right).$$

What are the best values of $K$ and $\gamma$ ? I have only the values $K=3$ and $\gamma=1/49152$ from Ellison and Mendès-France book Les nombres premiers (1975)

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