#### 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 Poincaré'' by J.F.~Ritt, on the differential transcendence of the solutions of the functional equation $$R(y(t))=y(qt)$$, where $$R(t)\in\mathbb C(t)$$ verifies $$R(0)=0$$, $$R'(0)=q\in\mathbb C$$, with $$|q|>1$$.
We also give a partial result in the case of an algebraic function $$R$$.

DOI:

ArXiv: 2102.08268

HAL: hal-03146286

Parent Category: Publications
Category: Preprints