Wronskien et équations différentielles p-adiques

Jean-Paul Bézivin

Acta Arithmetica (2013)

  • Volume: 158, Issue: 1, page 61-78
  • ISSN: 0065-1036

Abstract

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We prove an inequality linking the growth of a generalized Wronskian of m p-adic power series to the growth of the ordinary Wronskian of these m power series. A consequence is that if the Wronskian of m entire p-adic functions is a non-zero polynomial, then all these functions are polynomials. As an application, we prove that if a linear differential equation with coefficients in ℂₚ[x] has a complete system of solutions meromorphic in all ℂₚ, then all the solutions of the differential equation are rational functions. This is also the case when the linear differential equation has coefficients in ℚ[x], and has, for an infinity of prime numbers p, a complete system of meromorphic solutions in a disc of ℂₚ with radius strictly greater than 1.

How to cite

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Jean-Paul Bézivin. "Wronskien et équations différentielles p-adiques." Acta Arithmetica 158.1 (2013): 61-78. <http://eudml.org/doc/279095>.

@article{Jean2013,
author = {Jean-Paul Bézivin},
journal = {Acta Arithmetica},
keywords = {Wronskian; p-adic differential equation},
language = {fre},
number = {1},
pages = {61-78},
title = {Wronskien et équations différentielles p-adiques},
url = {http://eudml.org/doc/279095},
volume = {158},
year = {2013},
}

TY - JOUR
AU - Jean-Paul Bézivin
TI - Wronskien et équations différentielles p-adiques
JO - Acta Arithmetica
PY - 2013
VL - 158
IS - 1
SP - 61
EP - 78
LA - fre
KW - Wronskian; p-adic differential equation
UR - http://eudml.org/doc/279095
ER -

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