A representation theorem for a class of rigid analytic functions

Victor Alexandru; Nicolae Popescu; Alexandru Zaharescu

Journal de théorie des nombres de Bordeaux (2003)

  • Volume: 15, Issue: 3, page 639-650
  • ISSN: 1246-7405

Abstract

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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 = G a l c o n t ( p / p ) , where t is a lipschitzian element of p and C ( t , ϵ ) denotes the ϵ -neighborhood of the G -orbit of t .

How to cite

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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 -

References

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  1. [APZ1] V. Alexandru, N. Popescu, A. Zaharescu, On closed subfields of Cp. J. Number Theory68 (1998), 131-150. Zbl0901.11035MR1605907
  2. [APZ2] V. Alexandru, N. Popescu, A. Zaharescu, Trace on Cp. J. Number Theory88 (2001), 13-48. Zbl0965.11049MR1825989
  3. [Am] Y. Amice, Les nombres p-adiques, Presse Univ. de France, Collection Sup. 1975. Zbl0313.12104MR447195
  4. [Ax] J. Ax, Zeros of Polynomials over Local Fields - The Galois Action, J. Algebra15 (1970), 417-428. Zbl0216.04703MR263786
  5. [PZ] N. Popescu, A. Zaharescu, On the main invariant of an element over a local field, Portugaliae Mathematica54 (1997), 73—83. Zbl0894.11045MR1440129
  6. [Ar] E. Artin, Algebraic Numbers and Algebraic Functions, Gordon and Breach, New York/London/ Paris, 1967. Zbl0194.35301MR237460
  7. [FP] J. Fresnel, M. Van Der Put, Géometrie Analytique Rigide et Applications, Birkhäuser. Boston. Basel. Stuttgart, 1981. Zbl0479.14015MR644799

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