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

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In the present paper, we show that, for every δ>0, the function (L(s))⁽ᵐ⁾, where m∈ N ∪ { 0} and L (s):= ∑ₙ₌₁∞ a(n) n⁻ˢ is an element of the Selberg class S, takes any value infinitely often in any strip 1<(s) <1+δ, provided ∑ₚ≤ ₓ |a (p)|² κπ(x) for some κ>0. In particular, L (s) takes any non-zero value infinitely often in the strip 1<(s)<1+δ, and the first derivative of L (s) vanishes infinitely often.