Let $f(x)=\sum_{p\le x}\frac{1}{p}$ and $f_0(x)=\frac{1}{2}(f(x+0)+f(x-0))$. Then is there a (Riemann) explicit formula for $f_0(x)$ involving a sum over the non-trivial zeros ρ of the Riemann zeta function?
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1$\begingroup$ What is a "(Riemann) explicit formula"? $\endgroup$– LSpiceNov 16, 2018 at 21:07
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$\begingroup$ @LSpice A formula for $f_0(x)$ which is similar to en.wikipedia.org/wiki/Explicit_formulae_(L-function) $\endgroup$– BonbonNov 16, 2018 at 21:38
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$\begingroup$ What do you get from $\sum_p p^{-1} = \sum_{k \ge 1} \frac{\mu(k)}{k} \sum_{p^m \le x} \frac{p^{-mk}}{m}$ $\endgroup$– reunsNov 17, 2018 at 2:38
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