5 papers
Inhomogeneous order 1 iterative functional equations with applications to combinatorics
Lucia Di Vizio, Gwladys Fernandes, Marni Mishna
We show that if a Laurent series satisfies a particular kind of linear iterative equation, then is either a rational function or it is differentially tran…
A survey on the hypertranscendence of the solutions of the Schröder's, Böttcher's and Abel's equations
Gwladys Fernandes
In 1994, P.-G. Becker and W. Bergweiler listed all the differentially algebraic solutions of three famous functional equations: the Schr{ö}der's, B{ö}ttcher's and Abel's equations.…
Historical Developments of the Theory of Transcendence and Algebraic Independence
Gwladys Fernandes
Qu'est la majest{é} de ce qui finit, aupr{è}s des d{é}parts titubants, des d{é}sordres de l'aurore?. Let this question from the French writer Colette guide us to walk through the p…
A Galoisian proof of Ritt theorem on the differential transcendence of Poincaré functions
Lucia Di Vizio, Gwladys Fernandes
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 th…
Regular extensions and algebraic relations between values of Mahler functions in positive characteristic
Gwladys Fernandes
Let be a function field of characteristic . We recently established the analogue of a theorem of Ku. Nishioka for linear Mahler systems defined over $\mathbb{K}(z…