Rational solutions of linear differential equations

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 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision): 12 H 25, 11 B 37. © 1989, Australian Mathematical Society. All rights reserved.