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 δ>0δ>0, the function (log⁡L(s))(m)(log⁡L(s))(m), where m∈N∪{0}m∈N∪{0} and L(s):=∑n=1∞a(n)n−s is an element of the Selberg class SS, takes any value infinitely often in the strip 10κ>0. In particular, L(s)L(s) takes any non-zero value infinitely often in the strip 11Re(s)>1.