Open Access
Summer 2015 Julia’s equation and differential transcendence
Matthias Aschenbrenner, Walter Bergweiler
Illinois J. Math. 59(2): 277-294 (Summer 2015). DOI: 10.1215/ijm/1462450701


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. Our results apply, in particular, to the exponential generating function of a sequence arising from work of Shadrin and Zvonkine on Hurwitz numbers.


Download Citation

Matthias Aschenbrenner. Walter Bergweiler. "Julia’s equation and differential transcendence." Illinois J. Math. 59 (2) 277 - 294, Summer 2015.


Received: 24 July 2013; Revised: 30 September 2015; Published: Summer 2015
First available in Project Euclid: 5 May 2016

zbMATH: 1345.30029
MathSciNet: MR3499512
Digital Object Identifier: 10.1215/ijm/1462450701

Primary: 30D05 , 34M15

Rights: Copyright © 2015 University of Illinois at Urbana-Champaign

Vol.59 • No. 2 • Summer 2015
Back to Top