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A Galoisian proof of Ritt theorem on the differential transcendence of Poincar\'e functions

Abstract : Using Galois theory of functional equations, we give a new proof of the main result of the paper "Transcendental transcendency of certain functions of Poincar\'e" by J.F. Ritt, on the differential transcendence of the solutions of the functional equation R(y(t))=y(qt), where R is a rational function with complex coefficients which verifies R(0)=0, R'(0)=q, where q is a complex number with |q|>1. We also give a partial result in the case of an algebraic function R.
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https://hal.archives-ouvertes.fr/hal-03146286
Contributor : Lucia Di Vizio Connect in order to contact the contributor
Submitted on : Thursday, February 18, 2021 - 11:15:09 PM
Last modification on : Tuesday, January 4, 2022 - 6:39:05 AM

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  • HAL Id : hal-03146286, version 1
  • ARXIV : 2102.08268

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Lucia Di Vizio, Gwladys Fernandes. A Galoisian proof of Ritt theorem on the differential transcendence of Poincar\'e functions. 2021. ⟨hal-03146286⟩

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