J Austral Math Soc Ser A 46 pp184--196, 1989.

Rational Solutions of Linear Differential Equations

J.-P. Bezivin and P. Robba

Abstract

Let L be a linear differential operator with rational coefficients such that 0 is not an irregular singularity of L and that for sufficiently many p's the equation Lv = 0 has no zero solution mod p. We show that if u is a formal power series whose coefficients are p-adic integers for almost all p and if Lu is rational, then u too is rational.

1980 AMS Subject Classification (1985 Revision): 12H25, 11B37

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Authors

J.-P. Bezivin

Université Paris VI Math., Tour 45-46, 5ème étage, 4, place Jussieu, 75230 Paris Cedex 05, France.

P. Robba

Université Paris-Sud Math., Bâtiment 425, 91405 Orsay Cedex France.