Growth of solutions of linear differential equations at a logarithmic singularity
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- by A. Adolphson, B. Dwork and S. Sperber PDF
- Trans. Amer. Math. Soc. 271 (1982), 245-252 Request permission
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 $n - 1$.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 271 (1982), 245-252
- MSC: Primary 12H25; Secondary 12B40, 14G20, 34C11
- DOI: https://doi.org/10.1090/S0002-9947-1982-0648090-9
- MathSciNet review: 648090