= Real logarithmic derivative of Riemann xi
{title2=$\Re(\xi'/\xi)(\sigma+it)=\sum_\rho\frac{\sigma-\Re\rho}{(\sigma-\Re\rho)^2+(t-\Im\rho)^2}$}
Differentiate the genus-one <Hadamard factorization>. Its complex difference terms converge as $O(|\rho|^{-2})$, and the individual real sums converge by the <absolute convergence of the real xi logarithmic derivative>. The remaining constant is $\Re B+\sum\Re(1/\rho)$. On the <critical line> the xi <logarithmic derivative> has zero real part, while the kernel terms cancel in pairs reflected across that line. Hence this constant vanishes and gives the displayed formula away from zeros.
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