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Rational solutions of linear differential equations

Part of: Sequences and sets

Published online by Cambridge University Press:  09 April 2009

J.-P. Bezivin  and
P. Robba
J.-P. Bezivin
Affiliation:
Université ParisVI Math. Tour 45-46, 5ème étage 4, place Jussieu 75230 Paris Cedex 05, France
P. Robba
Affiliation:
Université Paris-Sud Math.Bâtiment 425 91405 Orsay Cedex, France
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Abstract

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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.

MSC classification

Secondary: 11B37: Recurrences
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 2 , April 1989 , pp. 184 - 196
Copyright
Copyright © Australian Mathematical Society 1989

References

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