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Let $ξ$ be a real number and let $n$ be a positive integer. We define four exponents of Diophantine approximation, which complement the exponents $w_{n} (ξ)$ and $w_{n}^{*} (ξ)$ defined by Mahler and Koksma. We calculate their six values when $n = 2$ and $ξ$ 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 $ξ$ by quadratic surds.

Displaying 1 – 7 of 7

Effective diophantine approximation on 𝔾 m

Effective diophantine approximation on 𝔾 M , II

Effective irrationality measures and approximation by algebraic conjugates

Effective measures for algebraic independence of the values of Mahler type functions

Ein Approximationsmaß für transzendente Lösungen gewisser transzendenter Gleichungen.

Erratum «Nouvelles méthodes pour minorer des combinaisons linéaires de logarithmes de nombres algébriques»

Exponents of Diophantine Approximation and Sturmian Continued Fractions

Currently displaying 1 – 7 of 7

Effective diophantine approximation on $𝔾_{m}$

Effective diophantine approximation on $𝔾_{M}$ , II