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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 $|\alpha - p(t)/q(t)| < |q(t){|^{ - 2 - 4m - \epsilon }}$.
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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