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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Growth of solutions of linear differential equations at a logarithmic singularity


Authors: A. Adolphson, B. Dwork and S. Sperber
Journal: Trans. Amer. Math. Soc. 271 (1982), 245-252
MSC: Primary 12H25; Secondary 12B40, 14G20, 34C11
MathSciNet review: 648090
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Abstract: We consider differential equations $ Y' = AY$ with a regular singular point at the origin, where $ A$ is an $ n \times n$ matrix whose entries are $ p$-adic meromorphic functions. If the solution matrix at the origin is of the form $ Y = P\exp (\theta \log x)$, where $ P$ is an $ n \times n$ matrix of meromorphic functions and $ \theta $ is an $ n \times n$ constant matrix whose Jordan normal form consists of a single block, then we prove that the entries of $ P$ have logarithmic growth of order $ n - 1$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0648090-9
PII: S 0002-9947(1982)0648090-9
Article copyright: © Copyright 1982 American Mathematical Society