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.
- D. N. Clark, A note on the $p$-adic convergence of solutions of linear differential equations, Proc. Amer. Math. Soc. 17 (1966), 262–269. MR 186895, DOI 10.1090/S0002-9939-1966-0186895-8
- W. H. Schikhof, Ultrametric calculus, Cambridge Studies in Advanced Mathematics, vol. 4, Cambridge University Press, Cambridge, 1984. An introduction to $p$-adic analysis. MR 791759
- M. Setoyanagi, On the convergence of solutions of $p$-adic linear differential equations, preprint.
- Minoru Setoyanagi
- Affiliation: Maizuru National College of Technology, 234 Shiraya, Maizuru, Kyoto 625, Japan
- Email: email@example.com
- Received by editor(s): October 8, 1995
- Communicated by: Dennis A. Hejhal
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 717-721
- MSC (1991): Primary 12H25; Secondary 11S80, 34G05
- DOI: https://doi.org/10.1090/S0002-9939-97-03983-X
- MathSciNet review: 1402887