Rational approximation to solutions of linear differential equations with algebraic coefficients
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- by Wolfgang M. Schmidt PDF
- Proc. Amer. Math. Soc. 53 (1975), 285-289 Request permission
Abstract:
Let $K$ be the field of formal series $\alpha = {a_k}{t^k} + \cdots + {a_0} + {a_{ - 1}}{t^{ - 1}} + \cdots$ and let $|\;\;|$ be the valuation with $|\alpha | = {2^k}$ if ${a_k} \ne 0$. Suppose $\alpha \epsilon K$ satisfies an $m{\text {th}}$ order linear differential equation whose coefficients are algebraic functions of $t$. Then for $\epsilon > 0$ there are only finitely many rational functions $p(t)/q(t)$ with $|\alpha - p(t)/q(t)| < |q(t){|^{ - 2 - 4m - \epsilon }}$.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 285-289
- MSC: Primary 10F45; Secondary 10F25
- DOI: https://doi.org/10.1090/S0002-9939-1975-0387210-2
- MathSciNet review: 0387210