Approximation by reduced fractions
نویسندگان
چکیده
منابع مشابه
Quadratic approximation to automatic continued fractions Sur l’approximation quadratique des fractions continues automatiques
We study the sets of values taken by the exponents of quadratic approximation w2 and w ∗ 2 evaluated at real numbers whose sequence of partial quotients is generated by a finite automaton. Among other results, we show that these sets contain every sufficiently large rational number and also some transcendental numbers. Résumé. Nous étudions les ensembles des valeurs prises par les exposants d’a...
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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...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1961
ISSN: 0025-5645
DOI: 10.2969/jmsj/01340342