Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Note on Clark's theorem for $p\,$ -adic convergence

Author(s): Minoru Setoyanagi
Journal: Proc. Amer. Math. Soc. 125 (1997), 717-721.
MSC (1991): Primary 12H25; Secondary 11S80, 34G05
MathSciNet review: 1402887
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Abstract: We must read Clark's statement under the hypothesis that the negative of each zero of the indicial polynomial is non-Liouville. In this note we shall give the example for which under the original hypothesis the statement does not hold.

References:

1.: D. N. Clark, A note on the -adic convergence of solutions of linear differential equations, Proc. Amer. Math. Soc. 17 (1966), 262-269. MR 32:4350
2.: W. Schikhof, Ultrametric calculus, Cambridge Univ. Press, Cambridge, 1984. MR 86j:11104
3.: M. Setoyanagi, On the convergence of solutions of -adic linear differential equations, preprint.

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