Value distribution for the derivatives of the logarithm of L-functions from the Selberg class in the half-plane of absolute convergence

In the present paper, we show that, for every $\delta>0$, the function $(\log {\mathcal{L}}(s))^{(m)}$, where $m\in {\mathbb{N}} \cup \{ 0\}$ and ${\mathcal{L}} (s) := \sum_{n=1}^\infty a(n) n^{-s}$ is an element of the Selberg class ${\mathcal{S}}$, takes any value infinitely often in any strip $1<\Re(s) <1+\delta$, provided $\sum_{p\leq x} |a (p)|^2 \sim \kappa\pi(x)$ for some $\kappa>0$. In particular, ${\mathcal{L}} (s)$ takes any non-zero value infinitely often in the strip $1<\Re(s)<1+\delta$, and the first derivative of ${\mathcal{L}} (s)$ vanishes infinitely often.