Hey simple question (I hope so), I´m reading Introduction to Analytic and Probabilistic Number Theory, and I don't get this step.
The author writes, this equation works by a "well known formula". But which is it, I don´t really get it?
$$ 2N(T) = \frac{1}{2\pi i } \int_R \frac{\xi^{\prime}(s)}{\xi(s)}\ ds = \frac{1}{2\pi} \Im\left(\int\limits_{R}\frac{\xi^{\prime}(s)}{\xi(s)}ds \right). $$
$\xi$ is the Riemann $\xi$-function and R is a rectangle with vertices $2+iT,~2-iT,~-1-iT,~-1+iT$ and N(T) is the number of zeros of $\xi$ till $\Im(s) \leq T$