EUDML

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Theorie de Nevanlinna p-adique.

Abdelbaki Boutabaa — 1990

Manuscripta mathematica

Applications de la théorie de Nevanlinna p-adique.

Abdelbaki Boutabaa — 1991

Collectanea Mathematica

Sur les courbes holomorphes $p$ -adiques

Abdelbaki Boutabaa — 1996

Annales de la Faculté des sciences de Toulouse : Mathématiques

Applications of the $p$ -adic Nevanlinna theory to functional equations

Abdelbaki Boutabaa; Alain Escassut — 2000

Annales de l'institut Fourier

Let $K$ be an algebraically closed field of characteristic zero, complete for an ultrametric absolute value. We apply the $p$ -adic Nevanlinna theory to functional equations of the form $g = R \circ f$ , where $R \in K (x)$ , $f, g$ are meromorphic functions in $K$ , or in an “open disk”, $g$ satisfying conditions on the order of its zeros and poles. In various cases we show that $f$ and $g$ must be constant when they are meromorphic in all $K$ , or they must be quotients of bounded functions when they are meromorphic in an “open disk”. In particular,...