A representation theorem for a class of rigid analytic functions
Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 3, pp. 639-650.

Soit p un nombre premier, p le corps des nombres p-adiques et p la complétion d’une clôture algébrique de p . Dans cet article, nous obtenons un théorème de représentation pour les fonctions analytiques rigides sur 𝐏 1 ( p )C(t,ϵ) qui sont équivariantes par le groupe de Galois G=Gal cont ( p / p ), où t désigne un élément lipschitzien de p et C(t,ϵ) un ϵ-voisinage de la G-orbite de t.

Let p be a prime number, p the field of p-adic numbers and p the completion of the algebraic closure of p . In this paper we obtain a representation theorem for rigid analytic functions on 𝐏 1 ( p )C(t,ϵ) which are equivariant with respect to the Galois group G=Gal cont ( p / p ), where t is a lipschitzian element of p and C(t,ϵ) denotes the ϵ-neighborhood of the G-orbit of t.

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     title = {A representation theorem for a class of rigid analytic functions},
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Alexandru, Victor; Popescu, Nicolae; Zaharescu, Alexandru. A representation theorem for a class of rigid analytic functions. Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 3, pp. 639-650. http://www.numdam.org/item/JTNB_2003__15_3_639_0/

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