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Article Dans Une Revue Annales de l'Institut Fourier Année : 2005

Exponents of Diophantine approximation and Sturmian continued fractions

Résumé

Let $\xi$ be a real number and let $n$ be a positive integer. We define four exponents of Diophantine approximation, which complement the exponents $w_n(\xi)$ and $w_n^*(\xi)$ defined by Mahler and Koksma. We calculate their six values when $n=2$ and $\xi$ is a real number whose continued fraction expansion coincides with some Sturmian sequence of positive integers, up to the initial terms. In particular, we obtain the exact exponent of approximation to such a continued fraction $\xi$ by quadratic surds.
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Dates et versions

hal-00088109 , version 1 (31-07-2006)

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  • HAL Id : hal-00088109 , version 1

Citer

Yann Bugeaud, Michel Laurent. Exponents of Diophantine approximation and Sturmian continued fractions. Annales de l'Institut Fourier, 2005, 55, num. 3, pp.773-804. ⟨hal-00088109⟩
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