On the value-distribution theorems for a class of $L$-functions

It is known that the values of $\log \zeta (1/2+it)$ are asymptotically Gaussian distributed. Namely, for any set $B \in \mathbb{C}$ of positive Jordan content, we have
\begin{equation*} \begin{split} \frac{1}{T} \text{ meas } \{ t\in [T; 2T] : \frac{\log \zeta(\frac12+it)}{\sqrt{\pi \log\log T}} \in B \} \sim \int\int_{B} e^{-\pi (x^2+y^2)} dx dy. \end{split} \end{equation*}
We shall talk about the proof of this type results for a class of L-functions and their applications (developed by Atle Selberg) to other problems on zeros of L-functions.