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On uniform approximation to real numbers
Yann Bugeaud 1   ; Johannes Schleischitz 2
1 IRMA, U.M.R. 7501 Université de Strasbourg et CNRS 7 rue René Descartes 67084 Strasbourg, France
2 Institute of Mathematics Department of Integrative Biology BOKU Wien 1180, Wien, Austria
Acta Arithmetica, Tome 175 (2016) no. 3, pp. 255-268 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa8372-7-2016
Keywords: integer transcendental real number establish several relations between values exponents diophantine approximation ast widehat widehat ast combining results recent estimates schmidt summerer allows refine inequality widehat n proved davenport schmidt

Yann Bugeaud  1   ; Johannes Schleischitz  2

1 IRMA, U.M.R. 7501 Université de Strasbourg et CNRS 7 rue René Descartes 67084 Strasbourg, France
2 Institute of Mathematics Department of Integrative Biology BOKU Wien 1180, Wien, Austria 
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Yann Bugeaud; Johannes Schleischitz. On uniform approximation to real numbers. Acta Arithmetica, Tome 175 (2016) no. 3, pp. 255-268. doi: 10.4064/aa8372-7-2016

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