Julia's equation and differential transcendence
Matthias Aschenbrenner, Walter Bergweiler
TL;DR
This paper proves that the iterative logarithm of non-linear entire functions is differentially transcendental over certain rings, providing criteria for this transcendence over convergent power series.
Contribution
It establishes the differential transcendence of iterative logarithms for non-linear entire functions and offers a criterion for this property over convergent power series.
Findings
Iterative logarithm of non-linear entire functions is differentially transcendental.
Provides a sufficient criterion for differential transcendence over convergent power series.
Advances understanding of the differential algebraic properties of iterative logarithms.
Abstract
We show that the iterative logarithm of each non-linear entire function is differentially transcendental over the ring of entire functions, and we give a sufficient criterion for such an iterative logarithm to be differentially transcendental over the ring of convergent power series.
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