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Can we prove that

$$\sum_{\exp((\log x)^{3/4})\le p\le x}\frac{1}{p^{1+it}}=o(\log\log x)$$

for $1\le t\le x$? Here $p$ runs over prime numbers.

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  • $\begingroup$ when $t$ is not too large, it is not so different to $\displaystyle\sum_{exp(\log^{3/4}x) < n < x} \frac{1}{n^{1+it} \ln n}$ $\endgroup$
    – reuns
    Aug 24, 2016 at 14:55

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