Analytic conductor (awaiting review)

The analytic conductor of an L-function $L(s)$ with infinity factor $L_{\infty}(s)$ and conductor $N$ is the real number \[ A := \mathrm{exp}\left(2\mathrm{Re}\left(\frac{L_{\infty}'(1/2)}{L_{\infty}(1/2)}\right)\right)N. \]