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On uniform approximation to real numbers

Volume 175 / 2016

Yann Bugeaud, Johannes Schleischitz Acta Arithmetica 175 (2016), 255-268 MSC: Primary 11J04; Secondary 11J13, 11J82. DOI: 10.4064/aa8372-7-2016 Published online: 23 September 2016

Abstract

Let $n \ge 2$ be an integer and $\xi$ a transcendental real number. We establish several new relations between the values at $\xi$ of the exponents of Diophantine approximation $w_n$, $w_{n}^{\ast}$, $\widehat{w}_{n}$, and $\widehat{w}_{n}^{\ast}$. Combining our results with recent estimates by Schmidt and Summerer allows us to refine the inequality $\widehat{w}_{n}(\xi) \le 2n-1$ proved by Davenport and Schmidt in 1969.

Authors

  • Yann BugeaudIRMA, U.M.R. 7501
    Université de Strasbourg et CNRS
    7 rue René Descartes
    67084 Strasbourg, France
    e-mail
  • Johannes SchleischitzInstitute of Mathematics
    Department of Integrative Biology
    BOKU Wien
    1180, Wien, Austria
    e-mail

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