A representation theorem for a class of rigid analytic functions

Alexandru, Victor, Popescu, Nicolae, and Zaharescu, Alexandru. "A representation theorem for a class of rigid analytic functions." Journal de théorie des nombres de Bordeaux 15.3 (2003): 639-650. <http://eudml.org/doc/249078>.

@article{Alexandru2003,
abstract = {Let $p$ be a prime number, $\mathbb \{Q\}_p$ the field of $p$-adic numbers and $\mathbb \{C\}_p$ the completion of the algebraic closure of $\mathbb \{Q\}_p$. In this paper we obtain a representation theorem for rigid analytic functions on $\mathbf \{P\}^1 (\mathbb \{C\}_p)\setminus C(t, \epsilon )$ which are equivariant with respect to the Galois group $G = Gal_\{cont\} (\mathbb \{C\}_p / \mathbb \{Q\}_p)$, where $t$ is a lipschitzian element of $\mathbb \{C\}_p$ and $C(t, \epsilon )$ denotes the $\epsilon $-neighborhood of the $G$-orbit of $t$.},
author = {Alexandru, Victor, Popescu, Nicolae, Zaharescu, Alexandru},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {rigid analytic functions; transcendental elements; Lipschitzian elements; -adic fields},
language = {eng},
number = {3},
pages = {639-650},
publisher = {Université Bordeaux I},
title = {A representation theorem for a class of rigid analytic functions},
url = {http://eudml.org/doc/249078},
volume = {15},
year = {2003},
}

TY - JOUR
AU - Alexandru, Victor
AU - Popescu, Nicolae
AU - Zaharescu, Alexandru
TI - A representation theorem for a class of rigid analytic functions
JO - Journal de théorie des nombres de Bordeaux
PY - 2003
PB - Université Bordeaux I
VL - 15
IS - 3
SP - 639
EP - 650
AB - Let $p$ be a prime number, $\mathbb {Q}_p$ the field of $p$-adic numbers and $\mathbb {C}_p$ the completion of the algebraic closure of $\mathbb {Q}_p$. In this paper we obtain a representation theorem for rigid analytic functions on $\mathbf {P}^1 (\mathbb {C}_p)\setminus C(t, \epsilon )$ which are equivariant with respect to the Galois group $G = Gal_{cont} (\mathbb {C}_p / \mathbb {Q}_p)$, where $t$ is a lipschitzian element of $\mathbb {C}_p$ and $C(t, \epsilon )$ denotes the $\epsilon $-neighborhood of the $G$-orbit of $t$.
LA - eng
KW - rigid analytic functions; transcendental elements; Lipschitzian elements; -adic fields
UR - http://eudml.org/doc/249078
ER -