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Une caracterisation des fonctions holomorphes injectives en analyse ultrametriqe

J. Rivera-Letelier
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Abstract

On montre qu'une fonction holomorphe non-constante $f$ definie sur un sous-espace analytique de $\CC_p$ est injective si et seulement si on a $$ | \frac{f(x) - f(y)}{{x - y)} |^2 = |f'(x) f'(y)|,$$ pour tous $x$ et $y$ distincts. Cette caracterisation demontre l'analogue, pour les fonctions holomorphes, d'une conjecture de A. Escassut et M.C. Sarmant. D'ature part on donne une contre-exemple a cette conjecture, qui concerne les elements bi-analytiques.

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J. Rivera-Letelier. 2002-05-07. Une caracterisation des fonctions holomorphes injectives en analyse ultrametriqe. https://arxiv.org/abs/math/0205070

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