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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

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

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

Information

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

Subjects:
Primary: 30D05, 34M15

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

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Vol.59 • No. 2 • Summer 2015
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