Universal uniqueness criterion II

[Kouznetsov]

2. Can we claim, that some of singularities of a modified tetration are at
\( \Re(z)>-2 \) ?

Dmitrii, modified tetration is not all, if you want to consider \( g(z)=f(J(z)) \) then you need to have a \( J \) first, a \( J=f^{-1}\circ g \) that is holomorphic on \( S \) which in turn imposes conditions on the cut, set in the domain of definition of \( f^{-1} \).

Sorry, I try again: If \( h \) is entire and 1-periodic and \( J(z)=z+h(z) \), then can we claim that \( \exists z \in \mathbb{C} ~:~ \Re(z)>-2 ~,~ J(z)\!=\!-2~.~ \) ?