Diophantine Approximations on Fractals
نویسندگان
چکیده
منابع مشابه
Report on Diophantine approximations
© Bulletin de la S. M. F., 1965, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impress...
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BY P. ERDOS, University of Syracuse . [Received 27 July, 1948 .] 1 . The present note contains some disconnected remarks on diophatine approximations . First we collect a few well-known results about continued fractions, which we shall use later' . Let a be an irrational number, q, < q2 < . . . be the sequence of the denominators of its convergents . For almost all a we have fork > k,,(a), qk+,...
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This article centres around the contributions of the author and therefore, it is confined to topics where the author has worked. Between these topics there are connections and we explain them by a result of Liouville in 1844 that for an algebraic number α of degree n ≥ 2, there exists c > 0 depending only on α such that | α− p q |> c qn for all rational numbers p q with q > 0. This inequality i...
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متن کاملProblems and results on diophantine approximations
The older literature on this subject (until about 1935) is treated in the excellent book of Koksma [1] . The more recent literature is discussed in a very interesting paper of Cigler and Helmberg [2] . Unlike the above authors I by no means aim to cover the literature completely and will mostly discuss only problems on which I myself worked thus a more exact title would have been "Problems and ...
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2011
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-011-0111-1