Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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


Author: Minoru Setoyanagi
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. 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 32:4350
  • 2. W. Schikhof, Ultrametric calculus, Cambridge Univ. Press, Cambridge, 1984. MR 86j:11104
  • 3. M. Setoyanagi, On the convergence of solutions of $p$-adic linear differential equations, preprint.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 12H25, 11S80, 34G05

Retrieve articles in all journals with MSC (1991): 12H25, 11S80, 34G05


Additional Information

Minoru Setoyanagi
Affiliation: Maizuru National College of Technology, 234 Shiraya, Maizuru, Kyoto 625, Japan
Email: set@maizuru-ct.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-97-03983-X
Keywords: $p$-adic convergence, $p$-adically non-Liouville number
Received by editor(s): October 8, 1995
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society